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On Laplacian Commutativity of Graphs
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This paper introduces the notion of Laplacian commutativity of graphs among well known classes of graphs. Two graphs are Laplacian commutative if their Laplacian matrices commute. The commutativity of the Laplacian matrix of a graph G
with its complement, G′
, and its k−
complement, GkP
is also examined. Laplacian commutativity depends on the partition P
of vertex set of G
, VG
and GkP
. Some necessary and sufficient conditions on the partition P
are described for the Laplacian commutativity of cycle Cn
with (Cn)Pk
.
Universiti Putra Malaysia
Title: On Laplacian Commutativity of Graphs
Description:
This paper introduces the notion of Laplacian commutativity of graphs among well known classes of graphs.
Two graphs are Laplacian commutative if their Laplacian matrices commute.
The commutativity of the Laplacian matrix of a graph G
with its complement, G′
, and its k−
complement, GkP
is also examined.
Laplacian commutativity depends on the partition P
of vertex set of G
, VG
and GkP
.
Some necessary and sufficient conditions on the partition P
are described for the Laplacian commutativity of cycle Cn
with (Cn)Pk
.
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