The Extremal Cacti on Multiplicative Degree-Kirchhoff Index

Fangguo He and Zhongxun Zhu
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Fangguo He: College of Mathematics and Physics, Huanggang Normal University, Huanggang 438000, China
Zhongxun Zhu: College of Mathematics and Statistics, South Central University for Nationalities, Wuhan 430074, China

Mathematics, 2019, vol. 7, issue 1, 1-12

Abstract: For a graph G , the resistance distance r G ( x , y ) is defined to be the effective resistance between vertices x and y , the multiplicative degree-Kirchhoff index R ∗ ( G ) = ∑ { x , y } ⊂ V ( G ) d G ( x ) d G ( y ) r G ( x , y ) , where d G ( x ) is the degree of vertex x , and V ( G ) denotes the vertex set of G . L. Feng et al. obtained the element in C a c t ( n ; t ) with first-minimum multiplicative degree-Kirchhoff index. In this paper, we first give some transformations on R ∗ ( G ) , and then, by these transformations, the second-minimum multiplicative degree-Kirchhoff index and the corresponding extremal graph are determined, respectively.

Keywords: resistance distance; multiplicative degree-Kirchhoff index; cactus (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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