Cordial And Product Cordial Labeling Of Edge Merged And Vertex Merged n-Chain Aztec Diamond Graphs

Abstract

A binary vertex labeling function $f$ from the vertices of a graph $G$ to ${\left\{0,1\right\}}$ is called cordial labeling, if each edge xy is given the label $\left|f(x)-f(y)\right|$, the resulting number of vertices with labels $0$ and the number of vertices with labels $1$ differ to the maximum of $1$, and the number of edge labels with $0$ and the number of edge labels with $1$ also differ to the maximum of $1$. In this paper $n$-chain edge merged and vertex merged Aztec diamond graphs are proved to be cordial but not product cordial.