diff --git a/include/graph/algorithm/breadth_first_search.hpp b/include/graph/algorithm/breadth_first_search.hpp
new file mode 100644
index 0000000..ed10d45
--- /dev/null
+++ b/include/graph/algorithm/breadth_first_search.hpp
@@ -0,0 +1,115 @@
+/**
+ * @file breadth_first_search.hpp
+ * 
+ * @brief Single-Source & multi-source breadth-first search.
+ * 
+ * @copyright Copyright (c) 2024
+ * 
+ * SPDX-License-Identifier: BSL-1.0
+ *
+ * @authors
+ */
+
+#include "graph/graph.hpp"
+#include "graph/views/incidence.hpp"
+
+#include <vector>
+#include <queue>
+#include <ranges>
+#include <limits>
+#include <fmt/format.h>
+
+#ifndef GRAPH_BREADTH_FIRST_SEARCH_HPP
+#  define GRAPH_BREADTH_FIRST_SEARCH_HPP
+
+namespace graph {
+
+using vertex_id_type = int;
+using Graph          = std::vector<std::vector<vertex_id_type>>;
+using Predecessors   = std::vector<vertex_id_type>;
+using Source         = vertex_id_type;
+using Sources        = std::vector<Source>;
+using Distance       = int;
+using Distances      = std::vector<Distance>;
+
+class dfs_visitor_base {
+  // Types
+public:
+  // Visitor Functions
+public:
+  // vertex visitor functions
+  void on_initialize_vertex(const vertex_id_type& uid) {}
+  void on_discover_vertex(const vertex_id_type& uid) {}
+  void on_examine_vertex(const vertex_id_type& uid) {}
+  void on_finish_vertex(const vertex_id_type& uid) {}
+
+  // edge visitor functions
+  void on_examine_edge(const vertex_id_type& uid) {}
+};
+
+/**
+ * @ingroup graph_algorithms
+ * @brief Returns the largest value used to represent an infinite distance.
+ * 
+ * @return The largest possible distance value.
+*/
+inline Distance bfs_infinite_distance() { return std::numeric_limits<Distance>::max(); }
+
+/**
+ * @ingroup graph_algorithms
+ * @brief Returns a distance value of zero.
+ * 
+ * @return A value of zero distance.
+*/
+inline Distance bfs_zero() { return 0; }
+
+/**
+ * @ingroup graph_algorithms
+ * @brief Intializes the distance values to the infinite value.
+ * 
+ * @param distances The range of distance values to initialize.
+*/
+inline void init_bfs(Distances& distances) {
+  for (size_t i = 0; i < distances.size(); ++i) {
+    distances[i] = bfs_infinite_distance();
+  }
+}
+
+/**
+ * @ingroup graph_algorithms
+ * @brief Intializes the distance and predecessor values for bfs.
+ * 
+ * @param distances The range of distance values to initialize. Each value will be assigned the infinite distance.
+ * @param predecessors The range of predecessors to initialize. Each value will be assigned the vertex id.
+*/
+inline void init_bfs(Distances& distances, Predecessors& predecessors) {
+  init_bfs(distances);
+  for (size_t i = 0; i < predecessors.size(); ++i) {
+    predecessors[i] = i;
+  }
+}
+
+/**
+ * @brief Single-source breadth-first search.
+ * 
+ * @param g            The graph.
+ * @param source	   The source vertex.
+ * @param predecessors The predecessor vertex for g[uid].
+ */
+
+// C++
+inline void
+breadth_first_search(const Graph& g, const Source& source, Distances& distances, Predecessors& predecessors) {}
+
+// C
+inline void breadth_first_search(const Graph*  g,
+                                 const Source  source,
+                                 const size_t  distances_len,
+                                 Distances*    distances,
+                                 const size_t  predecessors_len,
+                                 Predecessors* predecessors) {}
+
+
+} // namespace graph
+
+#endif // GRAPH_BREADTH_FIRST_SEARCH_HPP
diff --git a/include/graph/algorithm/depth_first_search.hpp b/include/graph/algorithm/depth_first_search.hpp
new file mode 100644
index 0000000..8dd65a0
--- /dev/null
+++ b/include/graph/algorithm/depth_first_search.hpp
@@ -0,0 +1,115 @@
+/**
+ * @file depth_first_search.hpp
+ * 
+ * @brief Single-Source & multi-source depth-first search.
+ * 
+ * @copyright Copyright (c) 2024
+ * 
+ * SPDX-License-Identifier: BSL-1.0
+ *
+ * @authors
+ */
+
+#include "graph/graph.hpp"
+#include "graph/views/incidence.hpp"
+
+#include <vector>
+#include <queue>
+#include <ranges>
+#include <limits>
+#include <fmt/format.h>
+
+#ifndef GRAPH_DFS_ALGORITHM_HPP
+#  define GRAPH_DFS_ALGORITHM_HPP
+
+namespace graph {
+
+using vertex_id_type = int;
+using Graph          = std::vector<std::vector<vertex_id_type>>;
+using Predecessors   = std::vector<vertex_id_type>;
+using Source         = vertex_id_type;
+using Sources        = std::vector<Source>;
+using Distance       = int;
+using Distances      = std::vector<Distance>;
+
+class dfs_visitor_base {
+  // Types
+public:
+  // Visitor Functions
+public:
+  // vertex visitor functions
+  void on_initialize_vertex(const vertex_id_type& uid) {}
+  void on_discover_vertex(const vertex_id_type& uid) {}
+  void on_examine_vertex(const vertex_id_type& uid) {}
+  void on_finish_vertex(const vertex_id_type& uid) {}
+
+  // edge visitor functions
+  void on_examine_edge(const vertex_id_type& uid) {}
+};
+
+/**
+ * @ingroup graph_algorithms
+ * @brief Returns the largest value used to represent an infinite distance.
+ * 
+ * @return The largest possible distance value.
+*/
+inline Distance dfs_infinite_distance() { return std::numeric_limits<Distance>::max(); }
+
+/**
+ * @ingroup graph_algorithms
+ * @brief Returns a distance value of zero.
+ * 
+ * @return A value of zero distance.
+*/
+inline Distance dfs_zero() { return 0; }
+
+/**
+ * @ingroup graph_algorithms
+ * @brief Intializes the distance values to the infinite value.
+ * 
+ * @param distances The range of distance values to initialize.
+*/
+inline void init_dfs(Distances& distances) {
+  for (size_t i = 0; i < distances.size(); ++i) {
+    distances[i] = dfs_infinite_distance();
+  }
+}
+
+/**
+ * @ingroup graph_algorithms
+ * @brief Intializes the distance and predecessor values for dfs.
+ * 
+ * @param distances The range of distance values to initialize. Each value will be assigned the infinite distance.
+ * @param predecessors The range of predecessors to initialize. Each value will be assigned the vertex id.
+*/
+inline void init_dfs(Distances& distances, Predecessors& predecessors) {
+  init_dfs(distances);
+  for (size_t i = 0; i < predecessors.size(); ++i) {
+    predecessors[i] = i;
+  }
+}
+
+/**
+ * @brief Single-source depth-first search.
+ * 
+ * @param g            The graph.
+ * @param source	   The source vertex.
+ * @param predecessors The predecessor vertex for g[uid].
+ */
+
+// C++
+inline void
+depth_first_search(const Graph& g, const Source& source, Distances& distances, Predecessors& predecessors) {}
+
+// C
+inline void depth_first_search(const Graph*  g,
+                                 const Source  source,
+                                 const size_t  distances_len,
+                                 Distances*    distances,
+                                 const size_t  predecessors_len,
+                                 Predecessors* predecessors) {}
+
+
+} // namespace graph
+
+#endif // GRAPH_DFS_ALGORITHM_HPP
diff --git a/include/graph/algorithm/dijkstra_shortest_paths.hpp b/include/graph/algorithm/dijkstra_shortest_paths.hpp
index 667d43e..c409f55 100644
--- a/include/graph/algorithm/dijkstra_shortest_paths.hpp
+++ b/include/graph/algorithm/dijkstra_shortest_paths.hpp
@@ -1,7 +1,7 @@
 /**
  * @file dijkstra_shortest_paths.hpp
  * 
- * @brief Single-Source Shortest paths and shortest distances algorithms using Dijkstra's algorithm.
+ * @brief Single-Source & multi-source shortest paths & shortest distances algorithms using Dijkstra's algorithm.
  * 
  * @copyright Copyright (c) 2024
  * 
diff --git a/include/graph/algorithm/topological_sort.hpp b/include/graph/algorithm/topological_sort.hpp
new file mode 100644
index 0000000..a58bc6a
--- /dev/null
+++ b/include/graph/algorithm/topological_sort.hpp
@@ -0,0 +1,114 @@
+/**
+ * @file topological_sort.hpp
+ * 
+ * @brief Single-Source & multi-source topological sort search.
+ * 
+ * @copyright Copyright (c) 2024
+ * 
+ * SPDX-License-Identifier: BSL-1.0
+ *
+ * @authors
+ */
+
+#include "graph/graph.hpp"
+#include "graph/views/incidence.hpp"
+
+#include <vector>
+#include <queue>
+#include <ranges>
+#include <limits>
+#include <fmt/format.h>
+
+#ifndef GRAPH_TOPO_SORT_ALGO_HPP
+#  define GRAPH_TOPO_SORT_ALGO_HPP
+
+namespace graph {
+
+using vertex_id_type = int;
+using Graph          = std::vector<std::vector<vertex_id_type>>;
+using Predecessors   = std::vector<vertex_id_type>;
+using Source         = vertex_id_type;
+using Sources        = std::vector<Source>;
+using Distance       = int;
+using Distances      = std::vector<Distance>;
+
+class topological_sort_visitor_base {
+  // Types
+public:
+  // Visitor Functions
+public:
+  // vertex visitor functions
+  void on_initialize_vertex(const vertex_id_type& uid) {}
+  void on_discover_vertex(const vertex_id_type& uid) {}
+  void on_examine_vertex(const vertex_id_type& uid) {}
+  void on_finish_vertex(const vertex_id_type& uid) {}
+
+  // edge visitor functions
+  void on_examine_edge(const vertex_id_type& uid) {}
+};
+
+/**
+ * @ingroup graph_algorithms
+ * @brief Returns the largest value used to represent an infinite distance.
+ * 
+ * @return The largest possible distance value.
+*/
+inline Distance topological_sort_infinite_distance() { return std::numeric_limits<Distance>::max(); }
+
+/**
+ * @ingroup graph_algorithms
+ * @brief Returns a distance value of zero.
+ * 
+ * @return A value of zero distance.
+*/
+inline Distance topological_sort_zero() { return 0; }
+
+/**
+ * @ingroup graph_algorithms
+ * @brief Intializes the distance values to the infinite value.
+ * 
+ * @param distances The range of distance values to initialize.
+*/
+inline void init_topological_sort(Distances& distances) {
+  for (size_t i = 0; i < distances.size(); ++i) {
+    distances[i] = topological_sort_infinite_distance();
+  }
+}
+
+/**
+ * @ingroup graph_algorithms
+ * @brief Intializes the distance and predecessor values for topological sort.
+ * 
+ * @param distances The range of distance values to initialize. Each value will be assigned the infinite distance.
+ * @param predecessors The range of predecessors to initialize. Each value will be assigned the vertex id.
+*/
+inline void init_topological_sort(Distances& distances, Predecessors& predecessors) {
+  init_topological_sort(distances);
+  for (size_t i = 0; i < predecessors.size(); ++i) {
+    predecessors[i] = i;
+  }
+}
+
+/**
+ * @brief Single-source topological sort.
+ * 
+ * @param g            The graph.
+ * @param source	   The source vertex.
+ * @param predecessors The predecessor vertex for g[uid].
+ */
+
+// C++
+inline void topological_sort(const Graph& g, const Source& source, Distances& distances, Predecessors& predecessors) {}
+
+// C
+inline void topological_sort(const Graph*  g,
+                             const Source  source,
+                             const size_t  distances_len,
+                             Distances*    distances,
+                             const size_t  predecessors_len,
+                             Predecessors* predecessors) {}
+
+
+} // namespace graph
+
+#endif // GRAPH_TOPO_SORT_ALGO_HPP
diff --git a/tests/CMakeLists.txt b/tests/CMakeLists.txt
index 49e35a9..f3a5021 100644
--- a/tests/CMakeLists.txt
+++ b/tests/CMakeLists.txt
@@ -36,6 +36,10 @@ set(UNITTEST_SOURCES
     "co_dijkstra_tests.cpp"
     "visitor_dijkstra_tests.cpp"
 
+    "breadth_first_search_tests.cpp"
+    "depth_first_search_tests.cpp"
+    "topological_sort_tests.cpp"
+
     "csv_routes_vofl_tests.cpp" 
     "csv_routes.cpp" 
     "csv_routes_dov_tests.cpp" 
diff --git a/tests/breadth_first_search_tests.cpp b/tests/breadth_first_search_tests.cpp
new file mode 100644
index 0000000..a90679b
--- /dev/null
+++ b/tests/breadth_first_search_tests.cpp
@@ -0,0 +1,48 @@
+#include <catch2/catch_test_macros.hpp>
+#include <catch2/catch_template_test_macros.hpp>
+#include "graph/algorithm/breadth_first_search.hpp"
+#include "graph/container/dynamic_graph.hpp"
+#include <iostream>
+
+#define GRAPH_BFS_ALGORITHM_HPP
+
+#define TEST_OPTION_OUTPUT (1)
+#define TEST_OPTION_GEN (2)
+#define TEST_OPTION_TEST (3)
+#define TEST_OPTION TEST_OPTION_TEST
+
+using std::cout;
+using std::endl;
+
+using std::ranges::forward_range;
+using std::forward_iterator;
+
+using namespace graph;
+
+void init_console(); // init cout for UTF-8
+
+TEST_CASE("breadth_first_search algorithm test", "[bfs][single-source][algorithm]") {
+  init_console();
+
+  // Create graph instance
+
+  SECTION("verify graph") {
+    // verify graph
+    REQUIRE(1 + 1 == 2);
+  }
+
+#if TEST_OPTION == TEST_OPTION_OUTPUT
+  SECTION("bfs algo output") {
+    // output graph
+    cout << "graph" << endl;
+  }
+#elif TEST_OPTION == TEST_OPTION_GEN
+  SECTION("bfs algo test generation") {
+    // generate test code
+  }
+#elif TEST_OPTION == TEST_OPTION_TEST
+  SECTION("bfs algo test") {
+    // production test code
+  }
+#endif // TEST_OPTION
+} // TEST_CASE"breadth_first_search algorithm test"
diff --git a/tests/depth_first_search_tests.cpp b/tests/depth_first_search_tests.cpp
new file mode 100644
index 0000000..552ce60
--- /dev/null
+++ b/tests/depth_first_search_tests.cpp
@@ -0,0 +1,47 @@
+#include <catch2/catch_test_macros.hpp>
+#include <catch2/catch_template_test_macros.hpp>
+#include "graph/algorithm/depth_first_search.hpp"
+#include "graph/container/dynamic_graph.hpp"
+#include <iostream>
+
+#  define TEST_OPTION_OUTPUT (1)
+#  define TEST_OPTION_GEN (2)
+#  define TEST_OPTION_TEST (3)
+#  define TEST_OPTION TEST_OPTION_TEST
+
+using std::cout;
+using std::endl;
+
+using std::ranges::forward_range;
+using std::forward_iterator;
+
+using namespace graph;
+
+void init_console(); // init cout for UTF-8
+
+TEST_CASE("depth_first_search algorithm test", "[bfs][single-source][algorithm]") {
+  init_console();
+
+  // Create graph instance
+
+  SECTION("verify graph") {
+    // verify graph
+    REQUIRE(1 + 1 == 2);
+  }
+
+#  if TEST_OPTION == TEST_OPTION_OUTPUT
+  SECTION("dfs algo output") {
+    // output graph
+    cout << "graph" << endl;
+  }
+#  elif TEST_OPTION == TEST_OPTION_GEN
+  SECTION("dfs algo test generation") {
+    // generate test code
+  }
+#  elif TEST_OPTION == TEST_OPTION_TEST
+  SECTION("dfs algo test") {
+    // production test code
+  }
+#  endif // TEST_OPTION
+} // TEST_CASE "depth_first_search algorithm test"
+
diff --git a/tests/topological_sort_tests.cpp b/tests/topological_sort_tests.cpp
new file mode 100644
index 0000000..d225ede
--- /dev/null
+++ b/tests/topological_sort_tests.cpp
@@ -0,0 +1,48 @@
+#include <catch2/catch_test_macros.hpp>
+#include <catch2/catch_template_test_macros.hpp>
+#include "graph/algorithm/topological_sort.hpp"
+#include "graph/container/dynamic_graph.hpp"
+#include <iostream>
+
+#define TEST_OPTION_OUTPUT (1)
+#define TEST_OPTION_GEN (2)
+#define TEST_OPTION_TEST (3)
+#define TEST_OPTION TEST_OPTION_TEST
+
+using std::cout;
+using std::endl;
+
+using std::ranges::forward_range;
+using std::forward_iterator;
+
+void init_console(); // init cout for UTF-8
+
+using namespace graph;
+
+void init_console(); // init cout for UTF-8
+
+TEST_CASE("topological_sort algorithm test", "[topo_sort][single-source][algorithm]") {
+  init_console();
+
+  // Create graph instance
+
+  SECTION("verify graph") {
+    // verify graph
+    REQUIRE(1 + 1 == 2);
+  }
+
+#if TEST_OPTION == TEST_OPTION_OUTPUT
+  SECTION("topo sort algo output") {
+    // output graph
+    cout << "graph" << endl;
+  }
+#elif TEST_OPTION == TEST_OPTION_GEN
+  SECTION("topo sort algo test generation") {
+    // generate test code
+  }
+#elif TEST_OPTION == TEST_OPTION_TEST
+  SECTION("topo sort algo test") {
+    // production test code
+  }
+#endif // TEST_OPTION
+} // TEST_CASE"topological_sort algorithm test"