Vertex-Addition Strategy for Domination-Like Invariants
Keyword(s):
In [J. Graph Theory 13 (1989) 749—762], McCuaig and Shepherd gave an upper bound of the domination number for connected graphs with minimum degree at least two. In this paper, we propose a simple strategy which, together with the McCuaig-Shepherd theorem, gives a sharp upper bound of the domination number via the number of leaves. We also apply the same strategy to other domination-like invariants, and find a relationship between such invariants and the number of leaves.
Keyword(s):
2012 ◽
Vol 2012
◽
pp. 1-7
◽
2019 ◽
Vol 29
(1)
◽
pp. 128-136
◽
Keyword(s):
2019 ◽
Vol 270
◽
pp. 159-167
◽
Keyword(s):
2021 ◽
Vol vol. 23 no. 1
(Graph Theory)
◽
Keyword(s):
Keyword(s):
2011 ◽
Vol Vol. 13 no. 3
(Graph Theory)
◽
Keyword(s):
2009 ◽
Vol 157
(13)
◽
pp. 2846-2858
◽
Keyword(s):