科研之友
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摘要
The edge-bandwidth of a graph G is the bandwidth of the line graph of G. Determining the edge-bandwidth B'(T-n) of triangular grids T-n is an open problem posed in 2006. Previously, an upper bound and an asymptotic lower bound were found to be 3n - 1 and 3n - o(n) respectively. In this paper we provide a lower bound 3n - [n/2] and show that it gives the exact values of B'(T-n) for 1 <= n <= 8 and n = 10. Also, we show the upper bound 3n - 5 for n >= 10.
