$delta^(k)$-colouring of cycle related graphs
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With respect to a proper colouring of a graph G, we know that 2≤χ(G)≤∆(G)+1. If distinct colours represent distinct technology types to be located at vertices, the question arises on how to place at least one of each of k, 1≤k<χ(G), technology types together with the minimum adjacency between similar technology types. In an improper colouring, an edge uv such that c(u) = c(v) is called a bad edge. In this paper, we introduce the notion of δ(k)-colouring which is a near proper colouring of G with exactly 1≤k < χ(G) distinct colours which minimizes the number of bad edges.
Abstract
With respect to a proper colouring of a graph G, we know that 2≤χ(G)≤∆(G)+1. If distinct colours represent distinct technology types to be located at vertices, the question arises on how to place at least one of each of k, 1≤k<χ(G), technology types together with the minimum adjacency between similar technology types. In an improper colouring, an edge uv such that c(u) = c(v) is called a bad edge. In this paper, we introduce the notion of δ(k)-colouring which is a near proper colouring of G with exactly 1≤k < χ(G) distinct colours which minimizes the number of bad edges.
참고문헌 (4)
- J.A. Bondy, "Graph theory" (1976), Springer
- F. Harary, "Graph theory" (2001), Narosa Publ. House
- Eunice Mphako-Banda, "An introduction to the <i>k<", i>-defect polynomials, 2018, pp.42(2), 207~216[DOI]
- D. B. West, "Introduction to graph theory" (2001), Prentice-Hall