Rainbow colouring of Oxide Networks

R Prabha, S Vasanthi

Abstract


A path in an edge coloured graph with no two edges sharing the same colour is called a rainbow path. The rainbow connection number $rc(G)$ of $G$ is the minimum integer $k$ for which there exists an $k-$ edge-coloring of $G$ such that every two distinct vertices of $G$ are connected by a rainbow path. It is known that computing the rainbow connection number of a graph is $NP-$Hard. So, it is interesting to compute $rc(G)$ for any given graph $G$. In this paper, we compute the rainbow connection number for oxide networks.


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References


M. Basavaraju, L.S. Chandran, D. Rajendraprasad and A. Ramaswamy, Rainbow Connection

number and radius, Graphs and Combinatories, Springer, 30(2)(2014), 275 - 285.

M. Basavaraju, L.S. Chandran, D. Rajendraprasad and A. Ramaswamy, Rainbow connection

number of graph power and graph products, Graphs and Combinatories, Springer, 30(6) 2014,

- 1382.

J.A. Bondy, U.S.R. Murty, GraphTheory, GTM 244, Springer, (2008).

S. Chakraborty, E. Fischer, A. Matsliah and R. Yuster, Hardness and algorithms for rainbow

connection, J. Combin. Optimization,(2009), 1 - 18.

L.S. Chandran, A. Das and D.Rajendraprasad, Rainbow Colouring of Split and Threshold

Graphs, Computing and Combinatorics, 7434(2012), 181-192.

G. Chartrand, G.L. Johns, K.A. McKeon and P. Zhang, Rainbow connection in graphs, Math.

Bohem, 133(2008), 85 - 98.

G. Chartrand, G.L. Johns, K.A. McKeon, P. Zhang, Rainbow connectivity of a graph, Networks,

(2009), 75-81.

Jasinthaquadras and S. Vasanthika, Rainbow colouring in Hexagonal Networks and Honeycomb

Networks, International conference on Mathematics in Engineering and Business Management

(2012), 208-211.

V.B. Le and Z. Tuza , Finding optimal rainbow connection is hard,(2009) preprint 24-28.

Paul Manuel and Indra Rajasingh, Minimum Metric Dimension of Silicate Networks, Proceedings

of the International Conference on Mathematics and Computer Science (2009), 46-50.

R. Prabha and Indra Rajasingh, Rainbow colouring of Crown Graphs, Journal of Computer

and Mathematical Sciences, 3(2)(2012), 248-421


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