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Published in:
2007 | OriginalPaper | Chapter
Hamiltonicity of Complements of Total Graphs
Authors : Guoyan Ma, Baoyindureng Wu
Published in: Discrete Geometry, Combinatorics and Graph Theory
Publisher: Springer Berlin Heidelberg
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For a graph
G
, the total graph
T
(
G
) of
G
is the graph with vertex set
V
(
G
) ∪
E
(
G
) in which the vertices
x
and
y
are joined by an edge if
x
and
y
are adjacent or incident in
G
. In this paper, we show that the complement of total graph
T
(
G
) of a simple graph
G
is hamiltonian if and only if
G
is not isomorphic to any graph in {
K
1,
r
|
r
≥ 1} ∪ {
K
1,
s
+
K
1
|
s
≥ 1} ∪ {
K
1,
t
+
e
|
t
≥ 2} ∪ {
K
2
+ 2
K
1
,
K
3
+ ,
K
1
,
K
3
+ 2
K
1
,
K
4
}.