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Vertex and edge PI indices of Cartesian product graphs

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CONTRIBUTORS:
  Author M. H. KHALIFEH
  Author Hassan YOUSEFI-AZARI
  Author Ali Reza ASHRAFI
JOURNAL:
  Discrete applied mathematics, 156(10), 1780 - 1789.
YEAR: 2008
PUB TYPE: Journal Article
SUBJECT(S): Combinatorics
DISCIPLINE: Mathematics
HTTP: http://lori.academicdirect.org/cites/200812.pdf
LANGUAGE: English
PUB ID: 103-445-933 (Last edited on 2009/11/09 07:48:09 US/Mountain)
SPONSOR(S):
 
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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