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Journal of Applied Mathematics and Computing

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19-12-2015 | Original Research

The largest Wiener index of unicyclic graphs given girth or maximum degree

Authors: Shang-wang Tan, Yan Lin

Published in: Journal of Applied Mathematics and Computing | Issue 1-2/2017

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Abstract

The Wiener index of a connected graph G is defined to be the sum of all distances of pairs of distinct vertices of G. Yu and Feng (Ars Comb 94:361–369, 2010) determined the unique graph having the largest Wiener index among all unicyclic graphs given girth. In the article we first give two new graphic transformations. Then with them we determine the graphs having the second largest Wiener index among all unicyclic graphs given girth and we also determine the graphs having the largest Wiener index among all unicyclic graphs given maximum degree.

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Title: The largest Wiener index of unicyclic graphs given girth or maximum degree
Authors: Shang-wang Tan
Yan Lin
Publication date: 19-12-2015
Publisher: Springer Berlin Heidelberg
Published in: Journal of Applied Mathematics and Computing / Issue 1-2/2017
Print ISSN: 1598-5865
Electronic ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-015-0971-x

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