Zagreb equienergetic bipartite graphs

Abstract

Let G be a graph with vertices v1, v2, . . . , vn and let di be the degree of vi. The Zagreb matrix of the graph G is the square matrix of order n whose (i, j)-entry is equal to di + dj if the vertices vi and vj are adjacent, and zero otherwise. The Zagreb energy ZE(G) of G is the sum of the absolute values of the eigenvalues of the Zagreb matrix. Two graphs are said to be Zagreb equienergetic if their Zagreb energies are equal. In this paper, we show how infinitely many pairs of Zagreb equienergetic bipartite graphs can be constructed such that these bipartite graphs are connected, possess an equal number of vertices, an equal number of edges, and are not cospectral.