LABEL INCIDENCE ENERGY OF PARTIAL EDGE LABELED GRAPH
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Let G = (V,E) be a simple graph with vertex set V = fv1, v2, . . . , vng and edge set E = fe1, e2, . . . , emg. The label incidence matrix Bl(G) of G is the n m matrix whose (i, j)-entry is a if 0 la- beled edge incident to 0 labeled vertex, b if 1 labeled edge incident to 1 labeled vertex, c if unlabeled edge incident to 0 or 1 labeled vertex and 0 otherwise. The label incidence energy IEl(G) is the sum of the singular values of Bl(G). In this paper we give lower and upper bounds for IEl(G) in terms of graph parameters and we study label incidence energy of some families of graph.
Abstract
Let G = (V,E) be a simple graph with vertex set V = fv1, v2, . . . , vng and edge set E = fe1, e2, . . . , emg. The label incidence matrix Bl(G) of G is the n m matrix whose (i, j)-entry is a if 0 la- beled edge incident to 0 labeled vertex, b if 1 labeled edge incident to 1 labeled vertex, c if unlabeled edge incident to 0 or 1 labeled vertex and 0 otherwise. The label incidence energy IEl(G) is the sum of the singular values of Bl(G). In this paper we give lower and upper bounds for IEl(G) in terms of graph parameters and we study label incidence energy of some families of graph.
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