TY - EJOUR
AB - Determining the size of a maximum independent set of a graph G, denoted by alpha(G), is an NP-hard problem. Therefore many attempts are made to find upper and lower bounds, or exact values of alpha(G) for special classes of graphs. This paper is aimed toward studying this problem for the class of generalized Petersen graphs. We find new upper and lower bounds and some exact values for alpha(P(n, k)). With a computer program we have obtained exact values for each n < 78. In [2] it is conjectured that the size of the minimum vertex cover, beta(P(n, k)), is less than or equal to n + inverted right perpendicular n/5 inverted left perpendicular, for all n and k with n > 2k. We prove this conjecture for some cases. In particular, we show that if n > 3k, the conjecture is valid. We checked the conjecture with our table for n < 78 and it had no inconsistency. Finally, we show that for every fixed k, alpha(P(n,k)) can be computed using an algorithm with running time O(n).
T1 - Independence number of generalized Petersen graphs
DA - 2016
AU - Besharati, Nazli
AU - Ebrahimi, J. B.
AU - Azadi, A.
JF - Ars Combinatoria
SP - 239-255
VL - 124
EP - 239-255
PB - Charles Babbage Res Ctr
PP - Winnipeg
ID - 217853
KW - Generalized Petersen Graphs
KW - Independent Set
KW - Tree Decomposition
SN - 0381-7032
ER -