On Super (a,d)-Edge-Antimagic Total Labeling of Special Types of Crown Graphs

Abstract

For a graph $G=(V,E)$, a bijection $f$ from $V(G)\cup E(G)\to \{1,2,\mathrm{\dots },|V(G)|+|E(G)|\}$ is called $(a,d)$-edge-antimagic total ($(a,d)$-EAT) labeling of $G$ if the edge-weights $w(xy)=f(x)+f(y)+f(xy),xy\in E(G)$, form an arithmetic progression starting from $a$ and having a common difference $d$, where $a>0$ and $d\ge 0$ are two fixed integers. An $(a,d)$-EAT labeling is called super $(a,d)$-EAT labeling if the vertices are labeled with the smallest possible numbers; that is, $f(V)=\{\mathrm{1,2},\dots ,|V(G)|\}$. In this paper, we study super $(a,d)$-EAT labeling of cycles with some pendant edges attached to different vertices of the cycle.