IJPAM: Volume 39, No. 2 (2007)

ON THE NUMBER OF k-INDEPENDENT SETS
IN SOME PRODUCTS OF GRAPHS

Andrzej W\loch$^1$, Iwona W\loch$^2$
$^{1,2}$Faculty of Mathematics and Applied Physics
Technical University of Rzeszów
Ul. W. Pola 2, Rzeszów, 35-959, POLAND
$^1$e-mail: awloch@prz.edu.pl
$^2$e-mail: iwloch@prz.edu.pl


Abstract.A subset $S\subset V(G)$ is $k$-independent if for each two distinct vertices from $S$ the distance between them is at least $k$. In this paper we determine the number of all $k$-independent sets in some product of graphs.

Received: April 17, 2007

AMS Subject Classification: 05C20

Key Words and Phrases: $k$-independent set, counting, graph products

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 39
Issue: 2