Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8900960 | Applied Mathematics and Computation | 2018 | 5 Pages |
Abstract
Given an integer 1â¯â¤â¯jâ¯<â¯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, 1â¯â¤â¯iâ¯â¤â¯j, have color 1 and all other edges have color 2. Cheng et al. (2017) 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, jâ¯â¥â¯2. In this note, we determine the number of different shortest proper paths in (j)-colored hypercubes for arbitrary j. Moreover, we obtain a more general result.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Lina Xue, Weihua Yang, Shurong Zhang,