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http://dx.doi.org/10.14317/jami.2017.059

RADIO NUMBER OF TRANSFORMATION GRAPHS OF A PATH

YOGALAKSHMI, S. (Department of Mathematics, Dr. Ambedkar Institute of Technology)
SOORYANARAYANA, B. (Department of Mathematics, Dr. Ambedkar Institute of Technology)
RAMYA, RAMYA (Department of Mathematics, Dr. Ambedkar Institute of Technology)

Publication Information

Journal of applied mathematics & informatics / v.35, no.1_2, 2017 , pp. 59-74 More about this Journal

Abstract

A radio labeling of a graph G is a function $f:V(G){\rightarrow}\{1,2,{\ldots},k\}$ with the property that ${\mid}f(u)-f(v){\mid}{\geq}1+diam(G)-d(u,v)$ for every pair of vertices $u,v{\in}V(G)$ , where diam(G) and d(u, v) are diameter and distance between u and v in the graph G respectively. The radio number of a graph G, denoted by rn(G), is the smallest integer k such that G admits a radio labeling. In this paper, we completely determine radio number of all transformation graphs of a path.

Keywords

radio-labeling; radio graceful graphs;

Citations & Related Records

Reference

1	Frud Buckley and Frank Harary, Distance in Graphs, Addison-Wesley, (1990).
2	Chandrakala, K. Manjula and B Sooryanarayana, The transformation graph $G^{xyz}$ , International J. of Math. Sci. Engg. Appls.(IJMSEA),ISSN 0973-9424, 3 (2009), pp. 249-259.
3	Chandru Hedge, Certain properties of graph invariants related to security and reliablility of a network, PhD Thesis, VTU, (2014).
4	Gary Chartrand, David Erwin, Ping Zhang, A graph labeling problem Suggested by FM Channel Restrictions, Bull. Inst. Combin. Appl. 43 (2005), 43-57.
5	Grary Chartrand, David Erwin, Frank Harary and Phing Zhang, Radio labelings of graphs, Bull. Inst. Combin. Appl. 33 (2001), 77-85.
6	Daphne Der-Fen Liu, Radio Number for Trees, Discrete Math. 308(7):1153-1164, (2008). DOI
7	P. Devadasa Rao, B. Sooryanaryana and Chandru Hedge, Radio number of $k^{th}$ power of a path, (Communicated).
8	W.K. Hale, Frequency assignment: theory and applications, Proc. IEEE 68 (1980), 1497-1514. DOI
9	D. Liu and M. Xie, Radio number for square of cycles, congr, Numer. 169 (2004) 105-125.
10	D. Liu and M. Xie, Radio number of square paths, Ars Combin. 90 (2009), 307-319
11	D. Liu and Xuding Zhu, Multilevel Distance Labelings for paths and cycles, SIAM J. Discrete Math. 19 (2005) 610-621. DOI
12	B. Sooryanarayana, Vishu Kumar. M, and Manjula K., Radio Number of Cube of a path, International J. Math. Combin. 1 (2010),05-29.
13	S.K. Vaidya and D.D. Bantva, Radio number for total graph of paths, ISRN combinatorics, 2013, pp 1-5.
14	B. Wu and J.Meng, Basic properies of total transformation graphs, J.Math. Study 34 (2001), 109-116.
15	BaoyindurengWu, Li Zhang, and Zhao Zhang, The transformation graph $g^{xyz}$ when xyz = - + +, Discrete Math. 296 (2005), 263-270. DOI
16	Lan Xu and Baoyindureng Wu, The transformation graph $G^{-+-}$ , Discrete Math., 308 (2008), 5144-5148. DOI
17	Phing Zhang, Radio labellings of Cycles, Ars Combin. 65 (2002), 21-32.