International Journal of Applied Mathematics and Computation | |
The neighbor coloring set in graphs | |
C. Nandeesh Kumar1  B. Chaluvaraju1  C. Appajigowda1  | |
[1] Department of Mathematics,Bangalore University, Central College Campus, Bangalore -560 001, India.$$ | |
关键词: Graph; neighborhood set; neighborhood numberneighbor-colorin; ; neighbor chromatic number; | |
DOI : 10.0000/ijamc.2012.4.3.424 | |
来源: PSIT Kanpur | |
【 摘 要 】
Given a graph $G=(V, E)$, a set $Ssubseteq V$ is a neighborhood set of $G$, if $G = igcup_{vin S}langle N[v]angle$, where $langle N[v]angle$ is the sub graph of $G$ induced by $v$ and all vertices adjacent to $v$. A neighborhood set $Ssubseteq V$ is said to be a neighbor coloring set of $G$ if each color class $V_{i}, 1leq i leq k$ contains at least one vertex, which belongs to $S$. The minimum cardinality taken over all neighbor coloring set of a graph $G$ is called neighbor chromatic number and is denoted by $chi_{eta}(G)$. In this paper, we study the properties of $chi_{eta}(G)$ and also its relationship with other graph theoretic parameters are explored.
【 授权许可】
Unknown
【 预 览 】
Files | Size | Format | View |
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RO201912040531195ZK.pdf | 239KB | download |