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The Vertex PI and Szeged Indices of Chain Graphs

Xianyong Li, Xiaofan Yang, Guoping Wang, Rongwei Hu

Open publisher page 9 citations

Abstract

The vertex Padmakar-Ivan ( PI v) index of a graph G was introduced as the sum over all edges e = uv of G of the number of vertices which are not equidistant to the vertices u and v. In this paper we provide an analogue to the results of T. Mansour and M. Schork (The PI index of bridge and chain graphs, MATCH Commun. Math. Comput. Chem .6 1 (2009) 723-734). Two efficient formulas for calculating the vertex PI index and Szeged index of chain graphs are determined. Using these formulas, the vertex PI index and Szeged index of a spiro chain of hexagons are computed.

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What this paper is about

The vertex Padmakar-Ivan ( PI v) index of a graph G was introduced as the sum over all edges e = uv of G of the number of vertices which are not equidistant to the vertices u and v. In this paper we provide an analogue to the results of T. Mansour and M. Schork (The PI index of bridge and chain graphs, MATCH Commun. Math. Comput. Chem .6 1 (2009) 723-734). Two efficient formulas for calculating the vertex PI index and Szeged index of chain graphs are determined. Using these formulas, the vertex PI index and Szeged index of a spiro chain of hexagons are computed.

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OpenAlex reports 9 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

The vertex Padmakar-Ivan ( PI v) index of a graph G was introduced as the sum over all edges e = uv of G of the number of vertices which are not equidistant to the vertices u and v. In this paper we provide an analogue to the results of T. Mansour and M. Schork (The PI index of bridge and chain graphs, MATCH Commun. Math. Comput. Chem .6 1 (2009) 723-734). Two efficient formulas for calculating the vertex PI index and Szeged index of chain graphs are determined. Using these formulas, the vertex PI index and Szeged index of a spiro chain of hexagons are computed.

Key concepts: Combinatorics, Vertex (graph theory), Mathematics, Pi, Equidistant, Graph, Index (typography), Chain (unit)

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