2019Quaestiones MathematicaeRequires access

Comparison between Szeged indices of graphs

Kinkar Chandra Das, Али Реза Ашрафи, Ali Ghalavand

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Abstract

The Szeged index Sz(G) of a simple connected graph G is the sum of the terms nu(e)nv (e) over all edges e = uv of G, where nu(e) is the number of vertices of G lying closer to u than v, and nv (e) is defined analogously. The aim of this paper is to present some relationship between Szeged index and some of its variants such as the edge-vertex Szeged index, the vertex-edge Szeged index and revised Szeged index. Moreover, we obtain lower and upper bounds on the difference between vertex-edge Szeged index and edge-vertex Szeged index of unicyclic graphs.

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What this paper is about

The Szeged index Sz(G) of a simple connected graph G is the sum of the terms nu(e)nv (e) over all edges e = uv of G, where nu(e) is the number of vertices of G lying closer to u than v, and nv (e) is defined analogously. The aim of this paper is to present some relationship between Szeged index and some of its variants such as the edge-vertex Szeged index, the vertex-edge Szeged index and revised Szeged index. Moreover, we obtain lower and upper bounds on the difference between vertex-edge Szeged index and edge-vertex Szeged index of unicyclic graphs.

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Available abstract

The Szeged index Sz(G) of a simple connected graph G is the sum of the terms nu(e)nv (e) over all edges e = uv of G, where nu(e) is the number of vertices of G lying closer to u than v, and nv (e) is defined analogously. The aim of this paper is to present some relationship between Szeged index and some of its variants such as the edge-vertex Szeged index, the vertex-edge Szeged index and revised Szeged index. Moreover, we obtain lower and upper bounds on the difference between vertex-edge Szeged index and edge-vertex Szeged index of unicyclic graphs.

Key concepts: Vertex (graph theory), Mathematics, Combinatorics, Index (typography), Graph, Connectivity, Enhanced Data Rates for GSM Evolution, Simple graph

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