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Fresán-Figueroa, J.; González-Moreno, D.; Olsen, M.
Discrete Applied Mathematics, 05/2023, Letnik: 331Journal Article
A generalized polygon is an incidence structure that satisfies certain regularity axioms and their incidence graphs are known as Moore graphs. For any fixed non-negative integer values h and k, a L(h,k)-coloring is a vertex coloring in which the difference between any pair of vertices at distance one is at least h and the any pair of vertices at distance two has coloring numbers that differ by at least k. The L(h,k)-span is the difference between the maximum and minimum color number. The goal of this problem is to find the L(h,k)-coloring with the smallest span. We present three structures of the generalized 2n-gons for n=3 and n=4 and use them to obtain bounds of the L(h,k)-number of their incidence graphs.
