Connective Steiner 3-eccentricity index and network similarity measure

Guihai Yu and Xingfu Li

Applied Mathematics and Computation, 2020, vol. 386, issue C

Abstract: For a set S⊆V(G) in a network G, the Steiner distance dG(S) of S is the minimum size among all connected subnetworks whose vertex sets contain S. The Steiner k-eccentricity ɛk(v) of a vertex v of G is the maximum Steiner distance among all k-vertex set S which contains the vertex v, i.e., εk(v)=max{d(S)|S⊆V(G),|S|=k,v∈S}. Based on Steiner k-eccentricity, the connective Steiner k-eccentricity index is introduced. As a newly structural invariant, some properties of the connective Steiner 3-eccentricity index are investigated. Firstly we present an O(n2)-polynomial time algorithm to calculate the connective Steiner 3-eccentricity index of trees. Secondly some optimal problems among some network classes are discussed. As its application, finally we consider the network similarity measure based on the connective Steiner 3-eccentricity index. By two different methods, we study its advantages. Numerical results show that the measure based on the connective Steiner 3-eccentricity index has more advantages than the ones based on other topological indices (graph energy, Randić index, the largest adjacent eigenvalue, the largest Laplacian eigenvalue).

Keywords: Steiner distance; Steiner k-eccentricity; Connective Steiner 3-eccentricity index (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:386:y:2020:i:c:s0096300320304070

DOI: 10.1016/j.amc.2020.125446

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