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Degree sums and proper connection number of graphs.
- Source :
-
Discrete Applied Mathematics . Nov2022, Vol. 321, p360-367. 8p. - Publication Year :
- 2022
-
Abstract
- An edge-colored graph G is called properly connected if any two vertices are connected by a properly colored path. The proper connection number of a graph G , denoted by p c (G) , is the smallest number of colors that are needed to color G such that it is properly connected. A separating vertex of G is bad if it is contained in at least three blocks, each of which contains at most three vertices. Let G be a graph of order n without bad vertices. In this paper, we show that if the degree sums of any three nonadjacent vertices of a graph G is at least 3 n / 4 and n > 48 , then p c (G) = 2 , which generalizes the results due to Borozan et al. (2012) and Chang et al. (2019). [ABSTRACT FROM AUTHOR]
- Subjects :
- *CHARTS, diagrams, etc.
*COLORS
*COLOR
Subjects
Details
- Language :
- English
- ISSN :
- 0166218X
- Volume :
- 321
- Database :
- Academic Search Index
- Journal :
- Discrete Applied Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 158957164
- Full Text :
- https://doi.org/10.1016/j.dam.2022.07.016