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Wiener and vertex PI indices of the strong product of graphs

K. Pattabiraman, P. Paulraja (2012)

Discussiones Mathematicae Graph Theory

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 ½ W ( G ) + ¼ u , v V ( G ) d ² 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 m , m , . . . , m r - 1 , where K m , m , . . . , m r - 1 is the complete multipartite graph with partite sets of sizes...

Wiener index of the tensor product of a path and a cycle

K. Pattabiraman, P. Paulraja (2011)

Discussiones Mathematicae Graph Theory

The Wiener index, denoted by W(G), of a connected graph G is the sum of all pairwise distances of vertices of the graph, that is, W ( G ) = ½ Σ u , v V ( G ) d ( u , v ) . In this paper, we obtain the Wiener index of the tensor product of a path and a cycle.

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