An Upper Bound For The Graovac-Pisanski(G-P) Index of The Fibonacci Cubes

Subject Areas : Statistics

Hojat Kaviani ¹ , LOTFALLAH POURFARAJ ^{2 *}

1 - Department of Mathematics, Central Tehran BranchIslamic Azad University,Tehran, Iran
2 - Department of Mathematics, Central Tehran Branch, Islamic AzadUniversity, Tehran, Iran

Received: 2021-09-18 Accepted : 2022-02-02 Published : 2024-01-18

Keywords: خودریختی گراف ها&quot, &quot, شاخص G-Pگراف &quot, , &quot, مکعب های فیبوناچی&quot, شاخص وینر گراف&quot,

Abstract :

Let G be a simple connected graph with vertex set V(G) and edge set E(G). A topological index of graph G is a numeric value to which the graph is assigned and is invariant to G automorphisms.The Wiener index of a connected graph G is defined as W(G) = ∑{u,v}⊆V (G) d(u, v) where d(u,v) is the distance between vertices u and v in G . The Graovac-Pisanski (G-P) index of a graph G is a modified version of the Wiener index on the distance between each vertex u and its image α(u) , where α is an automorphism of graph G . Let Fn be the set of all binary strings of length n that have no two consecutive 1s. The Fibonacci cube Γn ,where n>1or n=1, is a graph with the vertex set Fn . In this graph, two vertices are adjacent if and only if their differ be at precisely one coordinate. In this paper, we obtain an upper bound for the G-P index of the Fibonacci cubes.

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