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- Title
Proper (Strong) Rainbow Connection and Proper (Strong) Rainbow Vertex Connection of Some Special Graphs.
- Authors
Ma, Yingbin; Xue, Yanfeng; Zhang, Xiaoxue
- Abstract
The proper rainbow vertex connection number of G , denoted by p r v c (G) , is the smallest number of colors needed to properly color the vertices of G so that G is rainbow vertex connected. The proper strong rainbow vertex connection number of G , denoted by p s r v c (G) , is the smallest number of colors needed to properly color the vertices of G so that G is strong rainbow vertex connected. These two concepts are inspired by the concept of proper (strong) rainbow connection number of graphs. In this paper, we first determine the values of p r c (G) and p s r c (G) for some special graphs, such as all cubic graphs of order 8 , pencil graphs, circular ladders or Möbius ladders. Secondly, we obtain the values of p r v c (G) and p s r v c (G) for some special graphs, such as all cubic graphs of order 8 , paths, cycles, wheels, complete multipartite graphs, pencil graphs, circular ladders and Möbius ladders. Finally, we characterize all the connected graphs G with p r v c (G) = n and p r v c (G) = n − 1.
- Subjects
RAINBOWS; GRAPH coloring; COMPLETE graphs; GRAPH connectivity; RAMSEY numbers
- Publication
Journal of Interconnection Networks, 2023, Vol 23, Issue 3, p1
- ISSN
0219-2659
- Publication type
Article
- DOI
10.1142/S0219265922500062