Reflexive edge strength of convex polytopes and corona product of cycle with path

AIMS Mathematics

article

Kooi-Kuan Yoong¹  Roslan Hasni¹  Gee-Choon Lau²  Muhammad Ahsan Asim³  Ali Ahmad³ 

[1] Special Interest Group on Modelling and Data Analytics ,(SIGMDA), Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu;Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA ,(Segamat Campus);College of Computer Sciences and Information Technology, Jazan University

关键词: convex polytope;    corona product;    edge irregular reflexive labeling;    plane graph;    reflexive edge strength;   

DOI  :  10.3934/math.2022657

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

For a graph $ G $, we define a total $ k $-labeling $ \varphi $ is a combination of an edge labeling $ \varphi_e(x)\to\{1, 2, \ldots, k_e\} $ and a vertex labeling $ \varphi_v(x) \to \{0, 2, \ldots, 2k_v\} $, such that $ \varphi(x) = \varphi_v(x) $ if $ x\in V(G) $ and $ \varphi(x) = \varphi_e(x) $ if $ x\in E(G) $, then $ k = \, \mbox{max}\, \{k_e, 2k_v\} $. The total $ k $-labeling $ \varphi $ is an edge irregular reflexive $ k $-labeling of $ G $ if every two different edges $ xy $ and $ x^\prime y^\prime $, the edge weights are distinct. The smallest value $ k $ for which such labeling exists is called a reflexive edge strength of $ G $. In this paper, we focus on the edge irregular reflexive labeling of antiprism, convex polytopes $ \mathcal D_{n} $, $ \mathcal R_{n} $, and corona product of cycle with path. This study also leads to interesting open problems for further extension of the work.

【 授权许可】

CC BY