Harary energy of complement of line graphs of regular graphs
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Date
2020-12-31
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Ankara Üniversitesi Fen Fakültesi
Abstract
The Harary matrix of a graph
G
is defined as
H
(
G
)
=
[
h
i
j
]
, where
h
i
j
=
1
d
(
v
i
,
v
j
)
, if
i
≠
j
and
h
i
j
=
0
, otherwise, where
d
(
v
i
,
v
j
)
is the distance between the vertices
v
i
and
v
j
in
G
. The
H
-energy of
G
is defined as the sum of the absolute values of the eigenvalues of Harary matrix. Two graphs are said to be
H
-equienergetic if they have same
H
-energy. In this paper we obtain the
H
-energy of the complement of line graphs of certian regular graphs interms of the order and regularity of a graph and thus constructs pairs of
H
-equienergetic graphs of same order and having different
H
-eigenvalues.
Description
Keywords
Harary eigenvalues, Equienergetic graphs, Energy