Author:
Das K Ch,Akgüneş Nihat,Çevik A Sinan
Abstract
Abstract
Let us consider the finite monogenic semigroup
S
M
with zero having elements
{
x
,
x
2
,
x
3
,
…
,
x
n
}
. There exists an undirected graph
Γ
(
S
M
)
associated with
S
M
whose vertices are the non-zero elements
x
,
x
2
,
x
3
,
…
,
x
n
and, f or
1
≤
i
,
j
≤
n
, any two distinct vertices
x
i
and
x
j
are adjacent if
i
+
j
>
n
.
In this paper, the diameter, girth, maximum and minimum degrees, domination number, chromatic number, clique number, degree sequence, irregularity index and also perfectness of
Γ
(
S
M
)
have been established. In fact, some of the results obtained in this section are sharper and stricter than the results presented in DeMeyer et al. (Semigroup Forum 65:206-214, 2002). Moreover, the number of triangles for this special graph has been calculated. In the final part of the paper, by considering two (not necessarily different) graphs
Γ
(
S
M
1
)
and
Γ
(
S
M
2
)
, we present the spectral properties to the Cartesian product
Γ
(
S
M
1
)
□
Γ
(
S
M
2
)
.
MSC:05C10, 05C12, 06A07, 15A18, 15A36.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis
Cited by
20 articles.
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