3 -CONSTRAINED TOTAL LABELING OF A GRAPH

Abstract

A 3 - Constrained total labeling of a graph G(V, E) is a bijective mapping g : V UE  {1, 2, 3, . . . , |V | + |E|} with extra constraints | g(u) − g(v) | ≥ 3 , | g(u) − g(uv) | ≥ 3 and | g(uv) − g(vw) |≥ 3 whenever u, v, w ∈ V and uv, vw ∈ E. A graph G which admits such labeling is called a 3-Constrained total graph. In this paper we determine that Cn × P2, Double triangular snake graph, Chain sum graph of first kind, Helm graph, Sunlet graph, Wheel graph, Gear graph, Ladder graph, Dutch windmill graph, Triple triangular snake graph, Zig-Zag Graph and Double squared chain graph are 3 -Constrained total graphs.