Institutul de Matematică şi Informatică "Vladimir Andrunachievici"
Universitatea de Stat din MoldovaRO EN
Proper Magic Sigma Coloring of Specific Graphs
Authors: Panuvit Chuaephon, Kittikorn Nakprasit
Keywords: Graph coloring, proper magic sigma coloring, proper magic sigma chromatic number.
– 0.32 Mb
Keywords: Graph coloring, proper magic sigma coloring, proper magic sigma chromatic number.
Abstract
A coloring $\varphi: V(G)\rightarrow \{1,2,\ldots,k \}$ is called a \emph{magic sigma coloring} of $G$ if the sum of colors of all the vertices in the neighborhood of each vertex of $G$ is the same. A graph that admits such a coloring is said to be \emph{magic sigma colorable}. The minimum number $k$ required in a magic sigma coloring of a graph $G$ is called the \emph{magic sigma chromatic number}, denoted by $\sigma_{m}(G)$. These concepts have been extensively studied and motivate us to define a new type of coloring as follows. A coloring $\varphi: V(G)\rightarrow \{1,2,\ldots,k \}$ is called a \emph{proper magic sigma coloring} of $G$ if it is both a magic sigma coloring and a proper vertex coloring. The minimum number $k$ required for a proper magic sigma coloring of $G$ is called the \emph{proper magic sigma chromatic number}, denoted by $\sigma_{p,m}(G)$. In this work, we introduce the concept of the proper magic sigma chromatic number and study its properties. Additionally, we determine $\sigma_{p,m}(G)$ for several specific graphs.Panuvit Chuaephon
Department of Mathematics, Faculty of Science, Khon Kaen University
Khon Kaen, Thailand
E-mail:
Kittikorn Nakprasit
ORCID: https://orcid.org/0000-0002-0421-3631
Department of Mathematics, Faculty of Science, Khon Kaen University,
Khon Kaen, Thailand
Centre of Excellence in Mathematics, MHESI, Bangkok 10400, Thailand
E-mail:
Department of Mathematics, Faculty of Science, Khon Kaen University
Khon Kaen, Thailand
E-mail:
Kittikorn Nakprasit
ORCID: https://orcid.org/0000-0002-0421-3631
Department of Mathematics, Faculty of Science, Khon Kaen University,
Khon Kaen, Thailand
Centre of Excellence in Mathematics, MHESI, Bangkok 10400, Thailand
E-mail:
DOI
https://doi.org/10.56415/csjm.v33.08Fulltext
– 0.32 Mb
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