RAINBOW CONNECTION NUMBER
OF FLOWER SNARK GRAPH
K. Srinivasa Rao1,
U Vijaya Chandra Kumar2, Anjaneyulu Mekala3
1Department of Mathematics
Sri Venkateshwara College of Engineering
Bengaluru 562 157, INDIA
2 School of Applied Science (Mathematics)
REVA University, Bengaluru, INDIA
3 Gurunanak Institutions Technical Campus
Ibrahimpatnam, Hyderabad, INDIA

Abstract

Let $G$ be a nontrivial connected graph on which is defined a coloring $c:E(G)\rightarrow\{1,2,\cdots,k\},\,\,k\in N $ of the edges of $G$, where adjacent edges may be colored the same. A path in $G$ is called a rainbow path if no two edges of it are colored the same. $G$ is rainbow connected if $G$ contains a rainbow $u-v$ path for every two vertices $u$ and $v$ in it. The minimum $k$ for which there exists such a $k$-edge coloring is called the rainbow connection number of $G$, denoted by $rc(G)$.

In this paper we find the rainbow connection number of flower snark graph and their criticalness with respect to rainbow coloring.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 33
Issue: 4
Year: 2020

DOI: 10.12732/ijam.v33i4.4

Download Section



Download the full text of article from here.

You will need Adobe Acrobat reader. For more information and free download of the reader, please follow this link.

References

  1. [1] J.A. Bondy, U.S.R. Murty, Graph Theory, Springer (2008).
  2. [2] G. Chartrand, G.L. Johns, K.A. McKeon, P. Zhang, Rainbow connection in graphs, Mathematica Bohemica, 133, No 1 (2008), 85-98.
  3. [3] R. Isaacs, Infinite families of nontrivial trivalent graphs which are not Tait colorable, Amer. Math. Monthly, 82 (1975), 221239.
  4. [4] X. Li, Y. Shi, Y. Sun, Rainbow connection of graphs: A survey, Graphs Combin., 29, No 1 (2013), 1-38.
  5. [5] X. Li, Y. Sun, Rainbow Connection of Graphs, Springer-Verlag, New York (2012).
  6. [6] S. Nabila, A.N.M. Salmal, The rainbow connection number of Origami graphs and Pizza graphs, Procedia Computer Science, 74 (2015), 162-167.
  7. [7] I. Schiermeyer, Bounds for the rainbow connection number of graphs, Discussiones Mathematicae Graph Theory, 31, No 2 (2011), 387-395.
  8. [8] K. Srinivasa Rao, R. Murali, Rainbow critical graphs, Int. J. of Comp. Application, 4, No 4 (2014), 252-259.
  9. [9] K. Srinivasa Rao, R. Murali, S.K. Rajendra, Rainbow and strong rainbow criticalness of some standard graphs, Int. J. of Mathematics and Computer Research, 3, No 1 (2015), 829-836.
  10. [10] K. Srinivasa Rao, R. Murali, S.K. Rajendra, Rainbow connection number in brick product graphs, Bull. of the Internat. Math. Virtual Institute, 8 (2018), 55-66.
  11. [11] K. Srinivasa Rao, R. Murali, Rainbow connection number in brick product graphs C(2n,m, r), International J. of Math. Combin., 2 (2017), 70-83.
  12. [12] S. Sy, R. Wijaya, Surahamat, Rainbow connection of some graphs, Applied Mathematical Science, 8 (2014), 4693-4696.