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- W4317621294 abstract "The proper rainbow vertex connection number of [Formula: see text], denoted by [Formula: see text], is the smallest number of colors needed to properly color the vertices of [Formula: see text] so that [Formula: see text] is rainbow vertex connected. The proper strong rainbow vertex connection number of [Formula: see text], denoted by [Formula: see text], is the smallest number of colors needed to properly color the vertices of [Formula: see text] so that [Formula: see text] 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 [Formula: see text] and [Formula: see text] for some special graphs, such as all cubic graphs of order [Formula: see text], pencil graphs, circular ladders or Möbius ladders. Secondly, we obtain the values of [Formula: see text] and [Formula: see text] for some special graphs, such as all cubic graphs of order [Formula: see text], paths, cycles, wheels, complete multipartite graphs, pencil graphs, circular ladders and Möbius ladders. Finally, we characterize all the connected graphs [Formula: see text] with [Formula: see text] and [Formula: see text]." @default.
- W4317621294 created "2023-01-21" @default.
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- W4317621294 date "2023-01-20" @default.
- W4317621294 modified "2023-10-18" @default.
- W4317621294 title "Proper (Strong) Rainbow Connection and Proper (Strong) Rainbow Vertex Connection of Some Special Graphs" @default.
- W4317621294 doi "https://doi.org/10.1142/s0219265922500062" @default.
- W4317621294 hasPublicationYear "2023" @default.
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