Hamiltonicity of
3
t
EC
Graphs with
α
=
κ
+
1
Keyword(s):
A set S of vertices in a graph G is a total dominating set of G if every vertex of G is adjacent to some vertex in S . The minimum cardinality of a total dominating set of G is the total domination number γ t G of G . The graph G is total domination edge-critical, or γ t EC , if for every edge e in the complement of G , γ t G + e < γ t G . If G is γ t EC and γ t G = k , we say that G is k t EC . In this paper, we show that every 3 t EC graph with δ G ≥ 2 and α G = κ G + 1 has a Hamilton cycle.
2019 ◽
Vol 11
(01)
◽
pp. 1950004
2020 ◽
Vol 8
(4S5)
◽
pp. 272-276
Keyword(s):
2011 ◽
Vol 3
(3)
◽
pp. 547-555
◽
2020 ◽
Vol 8
(4S5)
◽
pp. 221-226
2021 ◽
Vol 14
(2)
◽
pp. 578-589