Odd Vertex equitable even labeling of cyclic snake related graphs.
Keywords:
vertex equitable labeling, vertex equitable graph, odd vertex equitable even labeling, odd vertex equitable even graphAbstract
Let G be a graph with p vertices and q edges and A = {1, 3, ..., q} if q is odd or A = {1, 3, ..., q + 1} if q is even. A graph G is said to admit an odd vertex equitable even labeling if there exists a vertex labeling f : V (G) → A that induces an edge labeling f∗ defined by f∗(uv) = f(u) + f(v) for all edges uv such that for all a and b in A, vf (a) − vf (b) ≤ 1 and the induced edge labels are 2, 4, ..., 2q where vf (a) be the number of vertices v with f(v) = a for a ∈ A. A graph that admits an odd vertex equitable even labeling is called an odd vertex equitable even graph. Here, we prove that the graph nC4snake, CS(n1, n2, ..., nk), ni ≡ 0(mod4),ni ≥ 4, be a generalized kCn snake, TÔQS_{n} and TÕQS_{n} are odd vertex equitable even graphs.
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