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2018 | 101 | 55-64
Article title

Radio Number of Cycles and their Total Graphs

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EN
Abstracts
EN
A radio labeling f of G is an assignment of positive integers to the vertices of G satisfying, │f (u) – f (v)│≥ diam(G) + 1 - d (u ,v) ∀ u, v ∈ V (G) where d (u ,v) is the distance between any two vertices in the graph. The radio number denoted by rn (G) is the minimum span of a radio labeling for G. In this paper, an alternate proof for radio number of cycles and exact radio number for their total graphs has been discussed.
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Year
Volume
101
Pages
55-64
Physical description
Contributors
author
  • Department of Mathematics, CHRIST (Deemed to be University), Bengaluru, Karnataka, India
  • Department of Mathematics, CHRIST (Deemed to be University), Bengaluru, Karnataka, India
References
  • [1] G. Chartrand et.al., Radio labelings of graph. Bull. Inst. Combin. Appl. 33 (2001) 77-85.
  • [2] W.K. Hale, Frequency assignment: theory and applications. Proceedings of the IEEE 68(12) (1980).
  • [3] D. Liu and X. Zhu, Multilevel distance labelings for paths and cycles. SIAM Journal on Discrete Mathematics 19(3) (2005) 610-621.
  • [4] T. A. Mangam and J.V. Kureethara, Diameteral Paths in Total Graph. Int. J. of pure and Appl. Math. 117(12) (2017) 273-280.
  • [5] F.S. Roberts, T-colorings of graphs: recent results and open problems. Discrete Mathematics 93(2-3) (1991) 229-245.
  • [6] D. Liu and M. Xie, Radio Number for Square paths. Ars Combinatoria, 90 (2009) 307-319.
  • [7] D. Liu and M. Xie, Radio Number for Square Cycles. Congr. Numerantium 169 (2004) 105-125.
  • [8] A. A. Bhatti et. al., Radio Number Of Wheel Like Graphs. Int. J. Appl. Graph, 3 (2011)
  • [9] S. K Vaidya and P L Vihol, Radio labeling for some cycle related graphs. International Journal of Mathematics and Soft Computing, 2 (2012) 11-24.
  • [10] S.K. Vaidya and D.D. Bantva, Radio Number for Total Graph of Paths. ISRN Comb. 2013 (2013) 1-5.
Document Type
article
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bwmeta1.element.psjd-c4869d9e-b58a-4a00-b8b6-3850ea83368f
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