The L(2,1)-Labeling of Some Middle Graphs

Abstract

An (2,1) L -labeling of a graph G is a function f from the vertex set V (G) to the set of all nonnegative integers such that |f(x)-f(y)| >= 2 if d(x,y) = 1 and |f(x)-f(y)| >= 1 if if d(x,y) = 2. The L(2,1) -labeling number λ(G) of G is the smallest number k such that G has an L(2,1)-labeling with max{f(v): v∈ V(G). In this paper we completely determine λ-number for middle graph of path Pn, cycle Cn , star K1,n , friendship graph Fn and wheel Wn.

Keywords

• L(2
• 1) -labeling
• λ -number
• Middle graphs