<jats:p>Let R be a commutative ring and let <jats:inline-formula>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="M1">
<mi mathvariant="normal">Γ</mi>
<mfenced open="(" close=")" separators="|">
<mrow>
<msub>
<mrow>
<mi>Z</mi>
</mrow>
<mrow>
<mi>n</mi>
</mrow>
</msub>
</mrow>
</mfenced>
</math>
</jats:inline-formula> be the zero divisor graph of a commutative ring <jats:inline-formula>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="M2">
<mi>R</mi>
</math>
</jats:inline-formula>, whose vertices are nonzero zero divisors of <jats:inline-formula>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="M3">
<msub>
<mrow>
<mi>Z</mi>
</mrow>
<mrow>
<mi>n</mi>
</mrow>
</msub>
</math>
</jats:inline-formula>, and such that the two vertices <jats:inline-formula>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="M4">
<mi>u</mi>
<mo>,</mo>
<mi>v</mi>
</math>
</jats:inline-formula> are adjacent if <jats:inline-formula>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="M5">
<mi>n</mi>
</math>
</jats:inline-formula> divides <jats:inline-formula>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="M6">
<mi>u</mi>
<mi>v</mi>
</math>
</jats:inline-formula>. In this paper, we introduce the concept of prime decomposition of zero divisor graph in a commutative ring and also discuss some special cases of <jats:inline-formula>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="M7">
<mi mathvariant="normal">Γ</mi>
<mfenced open="(" close=")" separators="|">
<mrow>
<msub>
<mrow>
<mi>Z</mi>
</mrow>
<mrow>
<mn>3</mn>
<mi>p</mi>
</mrow>
</msub>
</mrow>
</mfenced>
</math>
</jats:inline-formula>, <jats:inline-formula>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="M8">
<mi mathvariant="normal">Γ</mi>
<mfenced open="(" close=")" separators="|">
<mrow>
<msub>
<mrow>
<mi>Z</mi>
</mrow>
<mrow>
<mn>5</mn>
<mi>p</mi>
</mrow>
</msub>
</mrow>
</mfenced>
</math>
</jats:inline-formula>, <jats:inline-formula>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="M9">
<mi>Γ</mi>
<mfenced open="(" close=")" separators="|">
<mrow>
<msub>
<mrow>
<mi>Z</mi>
</mrow>
<mrow>
<mn>7</mn>
<mi>p</mi>
</mrow>
</msub>
</mrow>
</mfenced>
</math>
</jats:inline-formula>, and <jats:inline-formula>
<math xmlns="http://www.w3.org/1998/Math/MathML" id="M10">
<mi mathvariant="normal">Γ</mi>
<mfenced open="(" close=")" separators="|">
<mrow>
<msub>
<mrow>
<mi>Z</mi>
</mrow>
<mrow>
<mi>p</mi>
<mi>q</mi>
</mrow>
</msub>
</mrow>
</mfenced>
</math>
</jats:inline-formula>.</jats:p>
[1]
J. Sankar,et al.
DECOMPOSITION OF ZERO DIVISOR GRAPH IN A COMMUTATIVE RING
,
2020
.
[2]
Richard Hammack,et al.
A prime factor theorem for bipartite graphs
,
2015,
Eur. J. Comb..
[3]
Richard Hammack,et al.
On uniqueness of prime bipartite factors of graphs
,
2013,
Discret. Math..
[4]
V. M. Abraham,et al.
Decomposition of Graphs into Paths and Cycles
,
2013
.
[5]
D. O. Ajayi,et al.
Sunlet Decomposition of Certain Equipartite Graphs
,
2013
.
[6]
David F. Anderson,et al.
The Zero-Divisor Graph of a Commutative Ring☆
,
1999
.
[7]
I. Beck.
Coloring of commutative rings
,
1988
.
[8]
Elwood S. Buffa,et al.
Graph Theory with Applications
,
1977
.