Some transformations on multiplicative eccentricity resistance-distance and their applications

Yunchao Hong, Zhongxun Zhu and Amu Luo

Applied Mathematics and Computation, 2018, vol. 323, issue C, 75-85

Abstract: For a connected graph G, the multiplicative eccentricity resistance-distance is defined as ξR*(G)=∑{x,y}⊂V(G)ɛG(x)·ɛG(y)RG(x,y), where εG( · ) is the eccentricity of the corresponding vertex and RG(x, y) is the effective resistance between vertices x and y in G. A connected graph G is called a cactus if any two of its cycles have at most one common vertex. Let Cat(n; t) be the set of cacti possessing n vertices and t cycles, where 0≤t≤n−12. In this paper, we introduce some edge-grafting transformations which decrease ξR*(G). As their applications, the extremal graphs with minimum and second minimum ξR*(G)-value in Cat(n; t) are characterized.

Keywords: Eccentricity; Resistance-distance; Multiplicative eccentricity resistance-distance (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:323:y:2018:i:c:p:75-85

DOI: 10.1016/j.amc.2017.11.055

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