The Extremal Values and Rankings of the Gutman Index of k-Caterpillar

De-qiang WANG, Meng-meng FENG, Ke-lun WANG

Abstract


In this paper, based on the conception of the Gutman index of graphs, we proposed the degree-distance of a graph to a vertex and the vertex-Gutman index. We studied the extremal values and rankings of the vertex-Gutman indices of the k-caterpillar, obtained the distribution of the extremal vertices; we also researched the extremal values and rankings of the Gutman index of the family of k-caterpillar, characterized the corresponding extremal graphs.

Keywords


Gutman index, Vertex-Gutman index, k-Caterpillar, Extremal value, Ranking


DOI
10.12783/dtcse/cmsam2017/16374

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