WCSE 2017
ISBN: 978-981-11-3671-9 DOI: 10.18178/wcse.2017.06.188

The Minimal Kirchhoff Index Of Theta Shape Graph

Xiaomin Re, Jinyu Zou, Haizhen Ren

Abstract— The resistance distance between any two vertices of a connected graph G is defined as the effective resistance between them in the electrical network constructed from G by replacing each edge of G with unit resistor. Kirchhoff index is a structure-descriptor based on resistance distance. For the theta shape graphs(a specified class of bicycle graphs), the ordering rations of their Kirchhoff index remain open. In this paper, some new ordering relations are obtained by three graph transformations, and the minimal Kirchhoff index and the corresponding graph in this class of graphs is also discussed.

Index Terms— electrical network, resistance distance, Kirchhoff index, theta shape graph

Xiaomin Re, Haizhen Ren
Department of Mathematics, Qinghai Normal University, CHINA
Jinyu Zou
Department of Basic Courses, Qinghai University, CHINA

ISBN: 978-981-11-3671-9 DOI: 10.18178/wcse.2017.06.17Xsrc="http://www.wcse.org/uploadfile/2019/0823/20190823055609629.png" style="width: 120px; height: 68px;" />[Download]

Cite: Xiaomin Re, Jinyu Zou, Haizhen Ren, "The Minimal Kirchhoff Index Of Theta Shape Graph," Proceedings of 2017 the 7th International Workshop on Computer Science and Engineering, pp. 1084-1088, Beijing, 25-27 June, 2017.