Abstract.
Suppose G is a graph and T is a set of non-negative integers that contains 0. A T-coloring of G is an assignment of a non-negative integer f(x) to each vertex x of G such that |f(x)−f(y)|∉T whenever xy∈E(G). The edge span of a T-coloring−f is the maximum value of |f(x) f(y)| over all edges xy, and the T-edge span of a graph G is the minimum value of the edge span of a T-coloring of G. This paper studies the T-edge span of the dth power C d n of the n-cycle C n for T={0, 1, 2, …, k−1}. In particular, we find the exact value of the T-edge span of C n d for n≡0 or (mod d+1), and lower and upper bounds for other cases.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: May 13, 1996 Revised: December 8, 1997
Rights and permissions
About this article
Cite this article
Hu, SJ., Juan, ST. & Chang, G. T-Colorings and T-Edge Spans of Graphs. Graphs Comb 15, 295–301 (1999). https://doi.org/10.1007/s003730050063
Issue Date:
DOI: https://doi.org/10.1007/s003730050063