### A Study on Radio Labeling of Diameter N-2 and Caterpillar Graphs

#### Abstract

*Radio labeling of graphs is a specific type of graph labeling. The basic type of graph labeling is vertex coloring; this is where the vertices of a graph G are assigned different colors so that adjacent vertices are not given the same color. A k-coloring of a graph G is a coloring that uses k colors. The chromatic number of a graph G is the minimum value for k such that a k-coloring exists for G [2].*

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K. Benson, M. Porter, and M. Tomova. The Radio numbers of all graphs of order n and diameter n - 2. Le Matematiche.

Gary Chartrand. Introductory Graph Theory. Dover, 1977.

Gary Chartrand and Ping Zhang. Radio colorings of graphs|a survey. Int. J. Comput. Appl. Math., 2(3):237{252, 2007.

C. Fernandez, A. Flores, M. Tomova, and C. Wyels. The Radio Number of Gear Graphs. ArXiv e-prints, September 2008.

John P. Georges, David W. Mauro, and Marshall A. Whittlesey. Relating path coverings to vertex labellings with a condition at distance two. Discrete Math., 135(1-3):103{111, 1994.

W.K. Hale. Frequency assignment: Theory and applications. Proceedings of the IEEE, 68(12):1497 { 1514 dec. 1980.

Xiangwen Li, Vicky Mak, and Sanming Zhou. Optimal radio labellings of complete m-ary trees. Discrete Appl. Math., 158(5):507{515, 2010.

Daphne Der-Fen Liu. Radio number for trees. Discrete Math., 308(7):1153{1164, 2008.

Daphne Der-Fen Liu and Xuding Zhu. Multilevel distance labelings for paths and cycles. SIAM J. Discrete Math., 19(3):610{621 (electronic), 2005.

Ruxandra Marinescu-Ghemeci. Radio number for some thorn graphs. Discuss. Math. Graph Theory, 30(2):201{222, 2010.

Amanda Niedzialomski. Consecutive Radio Labelings and the Cartesian Product of Graphs. PhD thesis, The University of Iowa, 2013.

R.Ponraj, S.Sathish Narayanan and R.Kala, Radio mean number of some wheel related graphs, Jordan Journal of Mathematics and Statistics (JJMS), 7(4) (2014), 273286

R.Ponraj,S.Sathish Narayanan,” Radio mean number of some sub division graphs”, Jordan Journal of Mathematics and Statistics(JJMS) 9(1),2016 ,pp 45-64

DOI: https://doi.org/10.23956/ijermt.v6i8.115

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