Antipodal number of some powers of cycles

作者：Saha Laxman; Panigrahi Pratima^*

来源：Discrete Mathematics, 2012, 312(9): 1550-1557.

DOI：10.1016/j.disc.2011.10.032

• Antipodal number
• Channel assignment problem
• Radio k-coloring
• Radio k-chromatic number
• Span

For a simple connected graph G and an integer k with 1 %26lt;= k %26lt;= diam(G), a radio k-coloring of G is an assignment f of non-negative integers to the vertices of G such that vertical bar f (u) - f (nu)vertical bar %26gt;= k + 1 - d(u, nu) for each pair of distinct vertices u and nu of G, where diam(G) is the diameter of G and d(u, nu) is the distance between u and nu in G. The span of a radio k-coloring f is the largest integer assigned by f to a vertex of C. and the radio k-chromatic number of G, denoted by rc(k)(G), is the minimum of spans of all possible radio k-colorings of G. If k = diam(G) - 1, then rc(k)(G) is known as the antipodal number of G. In this paper, we give an upper and a lower bound of rc(k)(C-n(r)) for all possible values of n, k and r. Also we show that these bounds are sharp for antipodal number of C-n(r) for several values of n and r.

• 出版日期2012-5-6