The Radial Radio Number and the Clique Number of a Graph
Selvam Avadayappan1, M. Bhuvaneshwari2, S. Vimalajenifer3
1Selvam Avadayappan, Associate Professor, Research Centre of Mathematics, VHN Senthikumara Nadar College, Virudhunagar (Tamil Nadu), India.
2M. Bhuvaneshwari, Assistant Professor, Research Centre of Mathematics, VHN Senthikumara Nadar College, Virudhunagar (Tamil Nadu), India.
3S. Vimalajenifer, Research Scholar (F.T), Research Centre of Mathematics, VHN Senthikumara Nadar College, Virudhunagar (Tamil Nadu), India.
Manuscript received on 25 November 2019 | Revised Manuscript received on 19 December 2019 | Manuscript Published on 30 December 2019 | PP: 1002-1006 | Volume-9 Issue-1S4 December 2019 | Retrieval Number: A12151291S419/19©BEIESP | DOI: 10.35940/ijeat.A1215.1291S419
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: Let G(V(G),E(G)) be a graph. A radial radio labeling, f, of a connected graph G is an assignment of positive integers to the vertices satisfying the following condition: d(u, v) | f (u) f (v) | 1 r(G) , for any two distinct vertices u, v V(G) , where d(u,v) and r(G) denote the distance between the vertices u and v and the radius of the graph G, respectively. The span of a radial radio labeling f is the largest integer in the range of f and is denoted by span(f). The radial radio number of G, r(G) , is the minimum span taken over all radial radio labelingsof G. In this paper, we construct a graph a graph for which the difference between the radial radio number and the clique number is the given non negative integer.
Keywords: Diameter, Frequency Assignment Problem, Radius, Radio Labeling, Radio Number, Radial Radio Number, Radial Radio Number. AMS Subject Classification Code(2010):05C78.
Scope of the Article: Cognitive Radio Networks