Given this directed graph, which of the following statements is false? 1 2 3 4 5 6 7 8 There is a circuit of length 5 starting at vertex 2. There is a path of length 4 from vertex 5 to vertex 3. There is a walk of length 5 from vertex 5 to vertex 7. There is a cycle of length 3 starting at vertex 5.

Given a cycle graph Cn and a complete graph Kn on n vertices (n>3), select all the correct statements. The degree of each vertice in Cn is 2 The total number of edges in Kn is C(n, 2). The degree of each vertice in Kn is (n-1). The total number of edges in Cn is n.

Select the graph that is not regular. в D B D D C A B

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Given this directed graph, which of the following statements is true? 2 5 3 4 6 7 8 There is an edge from vertex 1 to vertex 2 in G³. There is an edge from vertex 1 to vertex 8 in G4. There is an edge from vertex 3 to vertex 4 in G². There is an edge from vertex 6 to vertex 7 in G².

In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints. In its simplest form, it is a way of coloring the vertices of a graph such that no two adjacent vertices share the same color; this is called a vertex coloring. The chromatic number of a graph is the least mumber of colors required to do a coloring of a graph. Example Here in this graph the chromatic number is 3 since we used 3 colors The degree of a vertex v in a graph (without loops) is the number of edges at v. If there are loops at v each loop contributes 2 to the valence of v. A graph is connected if for any pair of vertices u and v one can get from u to v by moving along the edges of the graph. Such routes that move along edges are known by different names: edge progressions, paths, simple paths, walks, trails, circuits, cycles, etc. a. Write down the degree of the 16 vertices in the graph below: 14…

Do it in PYTHON Language please!!