Cordial labeling on different types of nested triangular graphs

Abstract

A function $f: V(G) \to \{0, 1\}$ 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 $f:E(G) \to \{0, 1\}$ is defined as $f(e)=\left|f\left(u\right)-f(v)\right|$. Let ${\ v}_f\left(0\right),v_f(1)$ be the number of vertices of $G$ having labels 0 and 1 respectively under $f$ and $e_f\left(0\right),e_f(1)$ 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 $\left|v_f\left(0\right)-v_f(1)\right|\le 1 $ and $\left|e_f\left(0\right)-e_f(1)\right|\le 1$ . 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.