On super edge-antimagicness of connected generalized shackle of cycle with two chords

Abstract

Let $G$ be a simple graph of order $p$ and size $q$. The graph $G$ is called an {\it $(a,d)$-edge-antimagic total graph} 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 sequence with first term $a$ and common difference $d$. Such a graph is called {\it super} if the smallest possible labels appear on the vertices. In this paper we study a super edge-antimagicness of generalized shackle of cycle of order five with two chords, denoted by $gshack(C_5^2,v\in C_3,n)$. The result shows that the graph $gshack(C_5^2,v\in C_3,n)$ admits a super $(a,d)$-edge antimagic total labeling for some feasible $d\le 2$.