adjacency-matrix

Let A be the adjacency matrix of a simple undirected graph G. Suppose A is its own inverse. Which one of the following statements is always TRUE?

Let $A$ be the adjacency matrix of a simple undirected graph $G$. Suppose $A$ is its own inverse. Which one of the following statements is always TRUE?

Consider a simple undirected unweighted graph with at least three vertices. If A is the adjacency matrix of the graph, then the number of 3-cycles in the graph is given by the trac...

Which of the properties hold for the adjacency matrix A of a simple undirected unweighted graph having n vertices?

Let G(V, E) be a directed graph, where V = {1, 2, 3, 4, 5} is the set of vertices and E is the set of directed edges, as defined by the following adjacency matrix A. $$A[i][j] = \l...

Let G = (V, E) be an undirected unweighted connected graph. The diameter of G is defined as: diam(G) = $$\displaystyle\max_{u, x\in V}$$ {the length of shortest path between u and...

Consider the weighted undirected graph with $$4$$ vertices, where the weight of edge $$\left\{ {i,j} \right\}$$ is given by the entry $${W_{ij}}$$ in the matrix $$W.$$ $$$W = \left...

Let G be a graph with n vertices and m edges. What is the tightest upper bound on the running time of Depth First Search on G, when G is represented as an adjacency matrix?

Consider a complete undirected graph with vertex set {0, 1, 2, 3, 4}. Entry W(ij) in the matrix W below is the weight of the edge {i, j}. $$$w = \left( {\matrix{ 0 & 1 & 8 & 1 & 4...

Consider a complete undirected graph with vertex set {0,1,2,3,4}. Entry W ij in the matrix W below is the weight of the edge {i, j} $$$W = \left( {\matrix{ 0 & 1 & 8 & 1 & 4 \cr 1...

Consider a complete undirected graph with vertex set {0, 1, 2, 3, 4}. Entry W(ij) in the matrix W below is the weight of the edge {i, j}. $$$w = \left( {\matrix{ 0 & 1 & 8 & 1 & 4...