3-Total Sum Cordial Labeling on Some New Graphs

Abstract

Let \(G=(V,E)\) be a graph with vertex set \(V\) and edge set \(E\). Consider a vertex labeling \(f:V(G)\to \{0,1,2\}\) such that each edge \(uv\) assign the label \((f(u)+f(v)) (\{{\rm mod}\ 3)\). The map \(f\) is called a 3-total sum cordial labeling if \(|f(i)-f(j)|\le 1\), for \(i,j \in \{0,1,2\}\) where \(f(x)\) denotes the total number of vertices and edges labeled with \(x=\{0,1,2\}\). Any graph which satisfied 3-total sum cordial labeling is called a 3-total sum cordial graph. Here we prove some graphs like wheel, globe and a graph obtained by switching and duplication of arbitrary vertex of a cycle are 3-total sum cordial graphs.