Vertex Equitable Labeling of Cyclic Snakes and Bistar Graphs

Let G be a graph with p vertices and q edges and let A = {0, 1, 2,..., }. A vertex labeling f: V (G) ® A induces an edge labeling f * defined by f *(uv) = f(u) + f(v) for all edges uv. For , let vf (a) be the number of vertices v with f(v) = a. A graph G is said to be vertex equitable if there exists a vertex labeling f such that for all a and b in A, and the induced edge labels are 1, 2, 3, , q. In this paper, we establish vertex equitable labeling of square graph of and splitting graph of and kC4 –snake(k?1) and the generalized kCn –snake is vertex equitable if nº0(mod4),n?4. Keywords: Vertex equitable labeling; Vertex equitable graph. © 2014 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved. doi: http://dx.doi.org/10.3329/jsr.v6i1.15044 J. Sci. Res. 6 (1), 79-85 (2014)