L(2,1)-Labeling of Oxide and Silicate Networks

Kins Yenoke*, D. Francis Xavier and Temi Maryson

Department of Mathematics, Loyola College, Chennai-600 034, INDIA.


An L(2,1)-labeling of a graph G is a function from the vertex set V(G) to the set of all non-negative integers such that |𝑓(𝑢)−𝑓(𝑣)| ≥ 2 if 𝑑(𝑢,𝑣) = 1 and |𝑓(𝑢)−𝑓(𝑣)| ≥ 1 if 𝑑(𝑢,𝑣)=2, where 𝑑(𝑢,𝑣) denotes the distance between u and v in 𝐺. The L(2,1)-labeling number of 𝐺, denoted by 𝜆2,1(𝐺), is the smallest number k such that there is an L(2,1)-labeling with maximum label k. In this paper, we have determined the bounds for L(2,1)- labeling number of Oxide and Silicate networks.

Keywords :Labeling, L(2,1)-labeling, L(2,1)-labeling number, Oxide network, Silicate network.

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