INVERSE SUM INDEG ENERGY OF A GRAPH
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초록
Let G be a graph with n vertices and let di denote the degree of the vertex vi. For a given graph, there are more than 100 ma- trices obtained by using some properties of the graph. Most important and used ones are the adjacency, incidency and Laplacian matrices. Re- cently, several graph topological indices have been used in de ning new graph matrices. Graph energy is the quantity obtained as the sum of the absolute values of all eigenvalues of the adjacency matrix corresponding to the graph. Several types of energy have been de ned and applied in di erent applications by means of such graph matrices in place of the adjacency matrix. The inverse sum indeg matrix of a graph G is the n n matrix whose (i; j)-th entry is equal to didj di+dj if the ith and the jth vertices are adjacent and 0 otherwise. The inverse sum indeg energy ISIE(G) of G is similarly de ned as the sum of the absolute values of the eigenvalues of the inverse sum indeg matrix. In this paper, we compute the inverse sum indeg characteristic polynomial and the inverse sum indeg energy for standard graphs. Some properties and bounds for ISIE(G) are also obtained.
Abstract
Let G be a graph with n vertices and let di denote the degree of the vertex vi. For a given graph, there are more than 100 ma- trices obtained by using some properties of the graph. Most important and used ones are the adjacency, incidency and Laplacian matrices. Re- cently, several graph topological indices have been used in de ning new graph matrices. Graph energy is the quantity obtained as the sum of the absolute values of all eigenvalues of the adjacency matrix corresponding to the graph. Several types of energy have been de ned and applied in di erent applications by means of such graph matrices in place of the adjacency matrix. The inverse sum indeg matrix of a graph G is the n n matrix whose (i; j)-th entry is equal to didj di+dj if the ith and the jth vertices are adjacent and 0 otherwise. The inverse sum indeg energy ISIE(G) of G is similarly de ned as the sum of the absolute values of the eigenvalues of the inverse sum indeg matrix. In this paper, we compute the inverse sum indeg characteristic polynomial and the inverse sum indeg energy for standard graphs. Some properties and bounds for ISIE(G) are also obtained.
참고문헌 (10)
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