The b-Chromatic Number of Star Graph Families

• Main Authors: Vivin J. Vernold, M. Venkatachalam
• Format: Article
• Language: English
• Published: Università degli Studi di Catania 2010-12-01
• Series: Le Matematiche
• Subjects: Graph Theory; b-chromatic number; Star chromatic number; Achromatic number; Equitable chromatic number
• Online Access: http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/771
• ISSN: 0373-3505; 2037-5298

<span style="font-size: small; font-family: CMR10;"><span style="font-family: CMR10; font-size: small;"><p align="left">In this paper, we investigate the <span style="font-size: small; font-family: CMMI10;">b</span><span style="font-size: small; font-family: CMR10;">-chromatic number of central graph, middle graph and total graph of star graph, denoted by </span><em><span style="font-size: small; font-family: CMMI10;">C</span><span style="font-size: small; font-family: CMR10;">(</span><span style="font-size: small; font-family: CMMI10;">K</span><span style="font-size: xx-small; font-family: CMR8;">1</span><span style="font-size: xx-small; font-family: CMMI8;">,n</span><span style="font-size: small; font-family: CMR10;">)</span></em><span style="font-size: small; font-family: CMMI10;">, <em>M</em></span><em><span style="font-size: small; font-family: CMR10;">(</span><span style="font-size: small; font-family: CMMI10;">K</span><span style="font-size: xx-small; font-family: CMR8;">1</span><span style="font-size: xx-small; font-family: CMMI8;">,n</span></em><span style="font-size: small; font-family: CMR10;"><em>)</em>  and  </span><span style="font-size: small; font-family: CMMI10;"><em>T</em></span><em><span style="font-size: small; font-family: CMR10;">(</span><span style="font-size: small; font-family: CMMI10;">K</span><span style="font-size: xx-small; font-family: CMR8;">1</span><span style="font-size: xx-small; font-family: CMMI8;">,n</span></em><span style="font-size: small; font-family: CMR10;"><em>)</em> respectively. We discuss the relationship between </span><span style="font-size: small; font-family: CMMI10;">b</span><span style="font-size: small; font-family: CMR10;">-chromatic number with some other types of chromatic numbers such as chromatic number, star chromatic number and equitable chromatic number.</span></p></span></span>