Abstract
Let G be simple graph with n vertices and m edges. The energy E(G) of G, denotedby E(G), is dened to be the sum of the absolute values of the eigenvalues of G. Inthis paper, we present two new upper bounds for energy of a graph, one in terms ofm,n and another in terms of largest absolute eigenvalue and the smallest absoluteeigenvalue. The paper also contains upper bounds for Laplacian energy of graph.
Highlights
The concept of energy of a graph was introduced by I
Let G be a graph with n vertices {v1, v2, ..., vn} and m edges and A = be the adjacency matrix of the graph
The energy E(G) of G is defined to be the sum of the absolute values of the eigenvalues of G. i.e.,E(G) =
Summary
The concept of energy of a graph was introduced by I. The energy E(G) of G is defined to be the sum of the absolute values of the eigenvalues of G. i.e.,E(G) = The bounds for eigenvalues of graph can be found in [1,13]. Let μ1, μ2, · · · , μn be the Laplacian eigenvalues of G.
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