In:
Journal of Interconnection Networks, World Scientific Pub Co Pte Ltd, Vol. 23, No. 03 ( 2023-09)
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].
Type of Medium:
Online Resource
ISSN:
0219-2659
,
1793-6713
DOI:
10.1142/S0219265922500062
Language:
English
Publisher:
World Scientific Pub Co Pte Ltd
Publication Date:
2023
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