Vertex and edge PI indices of Cartesian product graphs |
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| Authors: | M.H. Khalifeh A.R. Ashrafi |
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| Affiliation: | a School of Mathematics, Statistics and Computer Science, University of Tehran, Tehran, Islamic Republic of Iran
b Department of Mathematics, Faculty of Science, University of Kashan, Kashan 87317-51167, Islamic Republic of Iran |
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| Abstract: | The Padmakar-Ivan (PI) index of a graph G is the sum over all edges uv of G of the number of edges which are not equidistant from u and v. In this paper, the notion of vertex PI index of a graph is introduced. We apply this notion to compute an exact expression for the PI index of Cartesian product of graphs. This extends a result by Klavzar [On the PI index: PI-partitions and Cartesian product graphs, MATCH Commun. Math. Comput. Chem. 57 (2007) 573-586] for bipartite graphs. Some important properties of vertex PI index are also investigated. |
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| Keywords: | 05C12 05A15 05A20 05C05 |
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