Super (a,d)-Edge-antimagic Total Labeling of Shakle of Fan Graph

Abstract

A graph $G$ of order $p$ and size $q$ is called an {\it $(a,d)$-edge-antimagic total} if there exist a bijection $f : V(G)\cup E(G) \to \{1,2,\dots,p+q\}$ such that the edge-weights, $w(uv)=f(u)+f(v)+f(uv), uv \in E(G)$, form an arithmetic sequencewith first term $a$ and common difference $d$. Such a graph $G$ is called {\it super} if the smallest possible labels appear on the vertices. In this paper we study super $(a,d)$-edge-antimagic total properties of connected  of amalgamation of Fan Graph. The result shows that amalgamation of Fan Graph admit a super edge antimagic total labeling for $d\in{0,1,2}$ for $n$ $\geq$ 1. It can be concluded that the result of this research has convered all the feasible $n$, $d$.