Network Energy: A New Energy of A Graph

The energy of the graph can be used estimating the altogether $\Pi$-electron energy of the given conjugated hydrocarbons, which was shown as the summation of absolute values of the whole eigenvalue of the adjacency matrix of the graph. We introduce a new energy of a graph in this literature and name it as network energy. On the basis of the number of the vertices for given graphs, we show several both lower bounds and upper bounds on network energy and establish upper bound to network energy on the basis of the probability and the number of the vertices for random graphs. Also several relations between the energy, the distance energy, the Laplacian-energy like invariant, the incidence energy and the matching energy of graphs are obtained.

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