Suppose G Is a Graph with Vertices A, B, C

question 126

Short Answer

Suppose G is a graph with vertices a, b, c, d, e, f with adjacency matrix $$\left( \begin{array} { l l l l l l } 0 & 1 & 0 & 1 & 0 & 0 \\1 & 0 & 0 & 1 & 1 & 1 \\0 & 0 & 0 & 0 & 1 & 1 \\1 & 1 & 0 & 0 & 1 & 0 \\0 & 1 & 1 & 1 & 0 & 1 \\0 & 1 & 1 & 0 & 1 & 0\end{array} \right)$$ (where alpha-
betical order is used to determine the rows and columns of the adjacency matrix). Find
(a) the number of vertices in
G.
(b) the number of edges in
G.
(c) the degree of each vertex.
(d) the number of loops.
(e) the length of the longest simple path in
G.
(f) the number of components in
G.
(g) the distance between vertex a and vertex c.
Questions 94-96 refer to a cubic graph, i.e., a graph that is simple and has every vertex of degree 3.

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