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- W4301478801 abstract "The b-chromatic number of a graph $G$, denoted by $phi(G)$, is the largest integer $k$ that $G$ admits a proper $k$-coloring such that each color class has a vertex that is adjacent to at least one vertex in each of the other color classes. We prove that for each $d$-regular graph $G$ which contains no 4-cycle, $phi(G)geqlfloorfrac{d+3}{2}rfloor$ and if $G$ has a triangle, then $phi(G)geqlfloorfrac{d+4}{2}rfloor$. Also, if $G$ is a $d$-regular graph which contains no 4-cycle and $diam(G)geq6$, then $phi(G)=d+1$. Finally, we show that for any $d$-regular graph $G$ which does not contain 4-cycle and $kappa(G)leqfrac{d+1}{2}$, $phi(G)=d+1$." @default.
- W4301478801 created "2022-10-05" @default.
- W4301478801 creator A5027894761 @default.
- W4301478801 date "2011-03-08" @default.
- W4301478801 modified "2023-09-27" @default.
- W4301478801 title "On The b-Chromatic Number of Regular Graphs Without 4-Cycle" @default.
- W4301478801 doi "https://doi.org/10.48550/arxiv.1103.1521" @default.
- W4301478801 hasPublicationYear "2011" @default.
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