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Radio numbers of some classes of GP(n, 1) and Cin(1, r)

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2 Author(s)
Kola, S.R. ; Dept. of Math., Rajiv Gandhi Univ. of Knowledge Technol., Hyderabad, India ; Panigrahi, P.

For any simple connected graph G with diameter d and an integer k, 1 ≤ k ≤ d, a radio k-coloring is an assignment f of positive integers to the vertices of G such that |f(u)-f(v)|≥, 1 + k - d(u, v), where u and v are any two distinct vertices of G and d(u, v) is the distance between u and v. The maximum color (positive integer) assigned by f to some vertex of G is called the span of f. The minimum of spans of all possible radio k-colorings of G is called the radio k-chromatic number of G, denoted by rck(G). For k = d, the coloring is called the radio coloring and the radio d-chromatic number is the radio number of G. In this article, we give a criteria for a radio coloring to be minimal. We use this technique to define minimal radio colorings of some classes of generalized Petersen graphs and circulant graphs and find their radio numbers.

Published in:

India Conference (INDICON), 2011 Annual IEEE

Date of Conference:

16-18 Dec. 2011