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Connective Steiner 3-eccentricity index and network similarity measure

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  • Yu, Guihai
  • Li, Xingfu

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).

Suggested Citation

  • Yu, Guihai & Li, Xingfu, 2020. "Connective Steiner 3-eccentricity index and network similarity measure," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    • Handle: RePEc:eee:apmaco:v:386:y:2020:i:c:s0096300320304070
    DOI: 10.1016/j.amc.2020.125446
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    References listed on IDEAS

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    1. Dehmer, Matthias & Emmert-Streib, Frank & Shi, Yongtang, 2015. "Graph distance measures based on topological indices revisited," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 623-633.
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