On local antimagic chromatic number of various join graphs

Document Type : Original paper

Authors

1 Kalasalingam Academy of Research and Education

2 Universiti Teknologi MARA, Faculty of Computer and Mathematical Sciences, 85100 Segamat, Johor, Malaysia

3 Director (n-CARDMATH) Kalasalingam University Anand Nagar, Krishnankoil-626 126 Tamil Nadu, India

4 Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong, P.R. China.

Abstract

A local antimagic edge labeling of a graph G=(V,E) is a bijection f:E→{1,2,…,|E|} such that the induced vertex labeling f+:V→Z given by f+(u)=∑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 χla(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 χla(G∨H), where H is either a cycle or the empty graph On=Kn―, satisfies a sharp upper bound. Using this we determine the value of χla(G∨H) for many wheel related graphs G.

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References

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Communications in Combinatorics and Optimization
Volume 8, Issue 4
December 2023
Pages 693-714

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