IEEE Access (Jan 2019)
Amalgamations and Cycle-Antimagicness
Abstract
A finite simple graph $G$ is called a $(c,d)$ - $H$ -antimagic if $G$ satisfies the following properties: (i) $G$ has an $H$ -covering by the family of subgraphs $H_{1},H_{2}, {\dots },H_{r}$ where every $H_{t}\cong H, 1\leq t\leq r$ , (ii) there exists a bijection $\beta: V\cup E \rightarrow \{1,2,3, {\dots },|V\cup E|\}$ such that the $H$ -weights constitute an arithmetic progression with initial term $c$ and common difference $d$ , where $c > 0, d \ge 0$ are integers. The labeling $\beta $ is called super if smallest possible labels appear on vertices of graph $G$ . For $m \in \mathbb {N}$ and $m \geq 2$ , let $\{G_{i}\}_{i=1}^{m}$ be a collection of graphs with $u_{i} \in V(G_{i})$ as a fixed vertex. The vertex amalgamation, denoted by $Amal(G_{i}, \{u_{i}\}, m)$ , is a graph formed by taking all the $G_{i}$ ’s and identifying $u_{i}$ ’s. In this research article, we studied super $(c,1)-C_{3}$ -antimagic labelings of amalgamation $Amal(G_{i}, \{u_{i}\}, m)$ of wheels, fans and flower graphs.
Keywords
