Total views : 281

### Rainbow Vertex Coloring for Line, Middle, Central, Total Graph of Comb Graph

#### Affiliations

• Faculty of Engineering and Technology, Department of Mathematics, SRM University, Kattankulathur - 603203, Tamil Nadu, India

#### Abstract

Objectives: To find the rainbow vertex connection number for Line, Central, Middle and Total graphs of Comb Graph. Methods/Statistical Analysis: The methods to find the rainbow vertex connection number of any graph G is quite different from other coloring problems. Findings: The rainbow vertex connection number for line graph and middle graph of comb graph      2 n is rainbow vertex connection number for Central graph of Comb graph is 2 and Total graph of Comb graph is     3 n if n=7, 11; is     3 n -1 if n=4k+11, k ≥ 1. While finding the achromatic number for any graph G , noting that no two adjacent vertices receives same color but in the case of rainbow vertex coloring we can assign same color to the adjacent vertices. Application/Improvements: The applications of rainbow vertex connection number are same as rainbow connection number.

#### Keywords

Central and Total Graph of Comb Graph, Line, Middle, Rainbow Vertex Coloring, Rainbow Vertex Connection Number

#### Full Text:

|  (PDF views: 186)

#### References

• Chartrand G, Johns GL, Mckeon KA, Zhang P. Rainbow connection in graphs. Math Bohem. 2008; 133(1):1–14.
• Chartrand C, Zhaung P. Chromatic Graph Theory. CRC Press; 2008.
• Krivelevich M, Yuster R. The rainbow connection of a graph is (at most) reciprocal to its minimum degree. J Graph Theory. 2009; 63(3):185–91.
• Harary F. Graph theory. Naraosa Publishing House; 2001.
• Saha A, Sambroni E, Bogerd J, Schulz RW, Gac FL, Lareyre JJ. The cell context influences rainbow trout gonadotropin receptors’ selectivity. Indian Journal of Science and Technology. 2011 Aug; 4(S8):1–2.
• Yano A, Jouanno E, Klopp C, Guiguen Y. Gene expression profiling during gonadal differentiation in rainbow trout (Oncorhynchusmykiss) using a Next Generation Sequencing (NGS) approach. Indian Journal of Science and Technology. 2011 Aug; 4(S8):1–6.
• Nicol B, Yano A, Jouanno E, Branthonne A, Fostier A, Guiguen Y. Follistatin is expressed along with aromatase in female gonads during sex differentiation in the rainbow trout. Indian Journal of Science and Technology. 2011 Aug; 4(S8):1–1.
• Valdivia K, Jouanno E, Mourot B, Quillet E, Guyomard R, Volff JN, Galiana-Arnoux D, Cauty C, Fostier A, Guiguen Y. Masculinization in rainbow trout carrying the mal mutation is temperature sensitive. Indian Journal of Science and Technology. 2011 Aug; 4(S8):1–1.
• Kusakabe M, Takei Y, Luckenbach JA. Relaxin-3 and relaxin/insulin-like family peptide receptor 3 in rainbow trout: Sites of gene expression and changes in messenger RNA levels during spermatogenesis in testes. Indian Journal of Science and Technology. 2011 Aug; 4(S8):1–2.

### Refbacks

• There are currently no refbacks.