Super (a,d)-edge-antimagic total labeling of connected Disc Brake graph

Abstract

Super edge-antimagic total labeling of a graph $G=(V,E)$ with order $p$ and size $q$, is a vertex labeling $\{1,2,3,...p\}$ and an edge labeling $\{p+1,p+2,...p+q\}$ such that the edge-weights, $w(uv)=f(u)+f(v)+f(uv), uv \in E(G)$ form an arithmetic sequence and for $a>0$ and $d\geq 0$, where $f(u)$ is a label of vertex $u$, $f(v)$ is a label of vertex $v$ and $f(uv)$ is a label of edge $uv$. In this paper we discuss about super edge-antimagic total labelings properties of connective Disc Brake graph, denoted by $Db_{n,p}$. The result shows that a connected Disc Brake graph admit a super $(a,d)$-edge antimagic total labeling for $d={0,1,2}$, $n\geq 3$, n is odd and $p\geq 2$. It can be concluded that the result has covered all the feasible $d$.