Proper Magic Sigma Coloring of Specific Graphs
A coloring $\varphi: V(G)\rightarrow \{1,2,\ldots,k \}$ is called a 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 magic sigma colorable. The minimum number $k$ required...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Vladimir Andrunachievici Institute of Mathematics and Computer Science
2025-04-01
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| Series: | Computer Science Journal of Moldova |
| Subjects: | |
| Online Access: | https://www.math.md/files/csjm/v33-n1/v33-n1-(pp141-156).pdf |
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| Summary: | A coloring $\varphi: V(G)\rightarrow \{1,2,\ldots,k \}$ is called a 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 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 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. |
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| ISSN: | 1561-4042 2587-4330 |