Graph Energy

Abstract

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Applications of a theorem by Ky Fan in the theory of weighted Laplacian graph energy

“…, λ n be eigenvalues of the adjacency matrix A(G) of graph G. It is known that ∑ n i=1 λ i = 0. The notion of the energy E (G) of an (n, m)-graph G was introduced by Gutman in connection with the π-molecular energy (see [13], [14], [16], [17], [21] and [29]). It is defined as…”

The Energy and Operations of Graphs

“…Up to now, the energy of G has been extensively studied, for details, we refer to [7] [8] [9]. In this paper, we determine the energy of graphs obtained from a graph by other unary operations, or graphs obtained from two graphs by other binary operations.…”

Upper bounds for the extended energy of graphs and some extended equienergetic graphs

“…In recent years, the concept of graph energy has been extensively studied by many researchers. Results on graph energy can be found in a book [12] by Li et al and references cited therein. Two graphs of same order are said to be equienergetic if their energies are same.…”