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Radio Degree of a Graph

Publication Type : Conference Proceedings

Publisher : AIP Conference Proceedings

Source : AIP Conference Proceedings, American Institute of Physics Inc., Volume 1952 (2018)

Url :

ISBN : 9780735416475

Campus : Bengaluru

School : School of Engineering

Department : Mathematics

Year : 2018

Abstract :

A labeling f: V (G) → Z+ such that |f(u) - f(v)|≥diam(G) + 1 - d(u, v) holds for every u, v ϵ V (G), is called a radio labeling of G. We define the radio degree of a labeling f: V (G) → {1, 2, ⋯ |V (G)|} as the number of pairs of vertices u, v ϵ V (G) satisfying the condition |f(u) - f(v)|≥diam(G) + 1 - d(u, v) and denote it by rdeg(f). The maximum value of rdeg(f) taken over all such labelings is defined as the radio degree of the graph denoted by rdeg(G). In this paper, we find the radio degree of some standard graphs like paths, cycles, complete graphs, complete bipartite graphs and also obtain a characterization of graphs of diameter two that achieve the maximum radio degree. © 2018 Author(s).

Cite this Research Publication : R. R. Vanam and Dr. K. N. Meera, “Radio degree of a graph”, in AIP Conference Proceedings, 2018, vol. 1952.

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