| Summary: | 碩士 === 中國文化大學 === 資訊管理學系 === 101 === Edge coloring of a graph is a function from its edge set to the set of natural numbers. A path in an edge colored graph with no two edges sharing the same color is called a rainbow path. An edge-colored graph is rainbow connected if any two vertices are connected by a rainbow path. Rainbow connection number is the minimum number of colors needed to color the edges of graph.
The concept of rainbow connection was introduced by Chartrand et al. in 2008. The rainbow connection problem is to find a vertex coloring for a given graph so that each pair of vertices of the graph having at least a rainbow path. As the characteristics and type of different network topologies are not the same, so we first devote ourselves to study a specify network topology. Then we find results of rainbow connection for the given graph.
Some results of rainbow connection for graphs were shown by the published papers, while the results for new network topologies were lack of discussion. As far as we know, the rainbow connection on Recursive Transpose-Connected Cycles pyramid networks is unknown
We consider the problem for Recursive Transpose-Connected Cycles pyramid networks, finally we propose a rainbow coloring for the RTCC pyramid networks based on 4-cycles. Then an upper bound of rainbow connection number is established for our studied interconnection networks.
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