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On local antimagic chromatic number of various join graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 7، دوره 8، شماره 4، اسفند 2023، صفحه 693-714 اصل مقاله (501.31 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2022.27937.1399 | ||
| نویسندگان | ||
| K. Premalatha1؛ Gee-Choon Lau2؛ Subramanian Arumugam* 3؛ W.C. Shiu4 | ||
| 1Kalasalingam Academy of Research and Education | ||
| 2Universiti Teknologi MARA, Faculty of Computer and Mathematical Sciences, 85100 Segamat, Johor, Malaysia | ||
| 3Director (n-CARDMATH) Kalasalingam University Anand Nagar, Krishnankoil-626 126 Tamil Nadu, India | ||
| 4Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong, P.R. China. | ||
| چکیده | ||
| A local antimagic edge labeling of a graph $G=(V,E)$ is a bijection $f:E\rightarrow\{1,2,\dots,|E|\}$ such that the induced vertex labeling $f^+:V\rightarrow \mathbb{Z}$ given by $f^+(u)=\sum f(e),$ where the summation runs over all edges $e$ incident to $u,$ has the property that any two adjacent vertices have distinct labels. A graph $G$ is said to be locally antimagic if it admits a local antimagic edge labeling. The local antimagic chromatic number $\chi_{la}(G)$ is the minimum number of distinct induced vertex labels over all local antimagic labelings of $G.$ In this paper we obtain sufficient conditions under which $\chi_{la}(G\vee H),$ where $H$ is either a cycle or the empty graph $O_n=\overline{K_n},$ satisfies a sharp upper bound. Using this we determine the value of $\chi_{la}(G\vee H)$ for many wheel related graphs $G.$ | ||
| کلیدواژه‌ها | ||
| Local antimagic chromatic number؛ join product؛ wheels؛ fans | ||
| مراجع | ||
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