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Wiener and vertex PI indices of the strong product of graphs

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Pattabiraman K., Paulraja P.

Discussiones Mathematicae Graph Theory

2012

tom 32

nr 4

749-769

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.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Pattabiraman K.

1 Paulraja P.

1 2012

Wyniki wyszukiwania

Wiener and vertex PI indices of the strong product of graphs