The L(2, 1)-Labeling on -Product of Graphs
نویسندگان
چکیده
Abstract. The L(2, 1)-labeling (or distance two labeling) of a graph G is an integer labeling of G in which two vertices at distance one from each other must have labels differing by at least 2 and those at distance two must differ by at least 1. The L(2, 1)labeling numberλ G of G is the smallest number k such that G has an L(2, 1)-labeling max{ ( ): ( )} f v v V G k ∈ = with max f v : v V G k. In this paper, upper bound for the L(2, 1)-labeling number for the α-product of two graphs has been obtained in terms of the maximum degrees of the graphs involved. Degrees of vertices, vertex of maximum degree and number of vertices of maximum degree have been discussed in the α-product of two graphs.
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