Local antimagic vertex coloring for generalized friendship graphs

Nalliah, M.; Shankar, R.; Wang, Tao-Ming

doi:10.1080/09720529.2021.1974651

Open Access Research Article

Local antimagic vertex coloring for generalized friendship graphs

M. Nalliahnalliahklu@gmail.comDepartment of MathematicsSchool of Advanced SciencesVellore Institute of TechnologyVellore, Tamil Nadu, 632014, IndiaView full profile → , R. Shankarrathinavelshankar@gmail.comDepartment of MathematicsSchool of Advanced SciencesVellore Institute of TechnologyVellore, Tamil Nadu, 632014, IndiaView full profile → , ^*Tao-Ming WangCorresponding authorwang@go.thu.edu.twDepartment of Applied MathematicsTunghai UniversityTaichung, 407224, Taiwan, R.O.C.View full profile →

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pp. 1063–1078Vol. 26Issue 4June 2023DOI: 10.1080/09720529.2021.1974651 Crossmark XML

Received:: 01 Mar 2021
Accepted:: 01 Jul 2021
Published Online:: 29 Mar 2022
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-1451
Pages:: 1063–1078

Abstract

Let G = (V, E) be a graph of order p and size q without isolated vertices. A bijection f: E → {1, 2, … , q} is called a local antimagic labeling if w(u) ≠ w(v) for all uv ∈ E, where the vertex weight w(u) = Ʃe∈E(u) f(e) and E(u) is the set of edges incident to the vertex u ∈ V. The local antimagic chromatic number χla(G) is defined to be the minimum number of colors(vertex weights) taken over all colorings of G induced by local antimagic labelings of G. In this paper, we study the local chromatic number for generalized friendship graph of complete graphs and cycles.

Keywords

Local antimagic labeling Local antimagic chromatic number Generalized friendship graph

Subject Classifications

(2020) 05C1505C78

References

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