On diameter and inverse degree of a graph |
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Authors: | Simon Mukwembi |
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Affiliation: | School of Mathematical Sciences, University of KwaZulu-Natal, Westville Campus, South Africa |
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Abstract: | The inverse degree r(G) of a finite graph G=(V,E) is defined as , where is the degree of vertex v. We establish inequalities concerning the sum of the diameter and the inverse degree of a graph which for the most part are tight. We also find upper bounds on the diameter of a graph in terms of its inverse degree for several important classes of graphs. For these classes, our results improve bounds by Erd?s et al. (1988) [5], and by Dankelmann et al. (2008) [4]. |
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Keywords: | Diameter Inverse degree Chemical graph |
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