Wiener and vertex PI indices of the strong product of graphs

• Autorzy: K. Pattabiraman , P. Paulraja
• Języki publikacji: EN

Abstrakty

EN

The Wiener index of a connected graph G, denoted by W(G), is defined as $½ ∑_{u,v ∈ V(G)}d_G(u,v)$. Similarly, the hyper-Wiener index of a connected graph G, denoted by WW(G), is defined as $½W(G) + ¼ ∑_{u,v ∈ V(G)} d²_G(u,v)$. The vertex Padmakar-Ivan (vertex PI) index of a graph G is the sum over all edges uv of G of the number of vertices which are not equidistant from u and v. In this paper, the exact formulae for Wiener, hyper-Wiener and vertex PI indices of the strong product $G ⊠ K_{m₀,m₁,...,m_{r -1}}$, where $K_{m₀,m₁,...,m_{r -1}}$ is the complete multipartite graph with partite sets of sizes $m₀,m₁, ...,m_{r -1}$, are obtained. Also lower bounds for Wiener and hyper-Wiener indices of strong product of graphs are established.

Słowa kluczowe

EN

strong product; Wiener index; hyper-Wiener index; vertex PI index

Kategorie tematyczne

• 05C12: Distance in graphs
• 05C76: Graph operations (line graphs, products, etc.)

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2012
• Tom: 32
• Numer: 4
• Strony: 749-769

Daty

wydano

2012

otrzymano

2011-06-20

poprawiono

2012-01-25

zaakceptowano

2012-01-27

Twórcy

autor

K. Pattabiraman

• Department of Mathematics, Annamalai University, Annamalainagar 608 002, India

autor

P. Paulraja

• Department of Mathematics, Annamalai University, Annamalainagar 608 002, India

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Identyfikatory

DOI

10.7151/dmgt.1647