A ug 2 01 7 On the number of proper paths between vertices in edge - colored hypercubes
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چکیده
Given an integer 1 ≤ j < n, define the (j)-coloring of a n-dimensional hypercube Hn to be the 2-coloring of the edges of Hn in which all edges in dimension i, 1 ≤ i ≤ j, have color 1 and all other edges have color 2. Cheng et al. [Proper distance in edge-colored hypercubes, Applied Mathematics and Computation 313 (2017) 384-391.] determined the number of distinct shortest properly colored paths between a pair of vertices for the (1)-colored hypercubes. It is natural to consider the number for (j)-coloring, j ≥ 2. In this note, we determine the number of different shortest proper paths in (j)-colored hypercubes for arbitrary j.
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تاریخ انتشار 2017