Advances and Applications in Discrete Mathematics
Volume 19, Issue 3, Pages 195 - 211
(July 2018) http://dx.doi.org/10.17654/DM019030195 |
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SPECTRAL STUDY OF THE INVERSE INDEX
Angel RamÃrez, Gerardo Reyna and Omar Rosario
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Abstract: Let be a simple graph of order n and size m with maximum degree D and minimum degree d and with no isolated vertices. The inverse index of G is defined as
where is the degree of the vertex In this paper, we obtain lower and upper bounds on of graph G and characterize graphs for which these bounds are best possible. Moreover, we compare inverse index with the topological index We also study the inverse index from an algebraic viewpoint. Since this index is related to the degree of the vertices of the graph, our main tool will be an appropriate matrix that is a modification of the classical adjacency matrix involving the degrees of the vertices. |
Keywords and phrases: inverse index, topological index, spectra of graphs, regular graphs. |
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