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 $(f(u)+f(v))(\{\mathrm{m}\mathrm{o}\mathrm{d}3)$. 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.