Cordial labeling on different types of nested triangular graphs ∗

Abstract

A function f : V (G) → {0, 1} is called the binary vertex labeling of a graph G and f(v) are called the labels of the vertex v of G under f. For an edge e = (u, v), the induced function f : E(G) → {0, 1} is defined as f(e) = |f (u) − f(v)|. Let vf (0), vf (1) be the number of vertices of G having labels 0 and 1 respectively under f and ef (0), ef (1) be the number of edges of G having labels 0 and 1 respectively under f. A binary vertex labeling f of a graph G is called cordial labeling if |vf (0) − vf (1)| ≤ 1 and |ef (0) − ef (1)| ≤ 1 . A graph which admits cordial labeling is called a cordial graph. In this paper we prove the cordial labeling for the Nested Triangle graph, the Shadow graph of the Nested Triangle graph and the double graph of the Nested Triangle graph.