The neighbor coloring set in graphs

International Journal of Applied Mathematics and Computation

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