Super (a,d)-H- Antimagic Total Coveringf on Shackle of Cycle with Cords

Abstract

Graph $G$ is a simple, finite and undirected graph. A graph $G$ is called to be an $(a,d)-H$-antimagic total covering if there is a bijective fuction $\lambda: V(G) \cup E(G) \rightarrow \{1, 2,\dots ,|V (G)| + |E(G)|\}$, such that for all subgraph $H'$ of $G$ isomorphic to $H$, where $\sum H'=\sum_{v \in V(H')}\lambda(v)+\sum_{e \in E(H')} \lambda(e)$ form an arithmetic sequence $\{a, a + d, a +2d,...,a+(s - 1)d\}$, where $a$ and $d$ are positive integers and $s$ is the number of all subgraphs $H'$ isomorphic to $H$. Graph $G$ will be called as $H$-antimagic super graph if $\{\lambda(v)\}{v \epsilon V}$ = $\{1, \ldots, \mid V \mid \}$. In this paper we will study about the existence of super $(a,d)-H$-antimagic total covering on shackle of cycle with cords denoted by $Shack$ $(C_6^3,e,n)$.