L(2,1)-Labeling for Subdivisions of Cycle Dominated Graphs

• Main Author: Muthali Murugan
• Format: Article
• Language: English
• Published: Universidad Simón Bolívar 2015-01-01
• Series: Bulletin of Computational Applied Mathematics
• Subjects: distance two labeling; transmitters; channel assignment; double fan
• Online Access: http://drive.google.com/open?id=0B5GyVVQ6O030cWRXLWMyMnRRMnM

Let G(V,E) be a simple, finite, connected, undirected graph. Distance two labeling or L(2,1)-labeling of a graph G is an assignment f from the vertex set V(G) to the set of non-negative integers such that |f(x)-f(y)| >= 2 if x and y are adjacent and |f(x)-f(y)| >= 1 if x and y are at distance 2, for all x and y in V(G). The L(2,1)-labeling number λ(G) of G is the smallest number k such that G has an L(2,1)-labeling f with max{f(v):v in V(G)}=k. In this paper, we construct L(2,1)-labeling of subdivisions of cycle dominated graphs like subdivided Double Fans, subdivided nCalpha with a common vertex and subdivided Books Bn and hence we find the λ-number of these graphs.