The Wiener index of the zero-divisor graph of Zn

2021 ◽  
Author(s):  
T. Asir ◽  
V. Rabikka
Keyword(s):  
Zero Divisor ◽  
Wiener Index ◽  
Zero Divisor Graph

scholarly journals Distance-Based Topological Polynomials Associated with Zero-Divisor Graphs

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Ali Ahmad ◽  
S. C. López
Keyword(s):  
Commutative Ring ◽  
Zero Divisor ◽  
Wiener Index ◽  
Formula One ◽  
Zero Divisor Graph ◽  
Zero Divisors ◽  
Vertex Set ◽  
Hosoya Polynomial ◽  
Nonzero Identity

Let R be a commutative ring with nonzero identity and let Z R be its set of zero divisors. The zero-divisor graph of R is the graph Γ R with vertex set V Γ R = Z R ∗ , where Z R ∗ = Z R \ 0 , and edge set E Γ R = x , y :   x ⋅ y = 0 . One of the basic results for these graphs is that Γ R is connected with diameter less than or equal to 3. In this paper, we obtain a few distance-based topological polynomials and indices of zero-divisor graph when the commutative ring is ℤ p 2 q 2 , namely, the Wiener index, the Hosoya polynomial, and the Shultz and the modified Shultz indices and polynomials.

scholarly journals On a new extension of the zero-divisor graph (II)

2021 ◽  
Author(s):  
A. Cherrabi ◽  
H. Essannouni ◽  
E. Jabbouri ◽  
A. Ouadfel
Keyword(s):  
Zero Divisor ◽  
Zero Divisor Graph

scholarly journals Sub-semigroups determined by the zero-divisor graph

2008 ◽  
Vol 308 (22) ◽  
pp. 5122-5135 ◽  
Author(s):  
Tongsuo Wu ◽  
Dancheng Lu
Keyword(s):  
Zero Divisor ◽  
Zero Divisor Graph

ON RINGS R WHOSE GRAPHS Γ(R) SATISFY CONDITION (Kp)

2011 ◽  
Vol 10 (04) ◽  
pp. 665-674
Author(s):  
LI CHEN ◽  
TONGSUO WU
Keyword(s):  
Prime Number ◽  
Commutative Ring ◽  
Complete Graph ◽  
Zero Divisor ◽  
Commutative Rings ◽  
Satisfy Condition ◽  
Induced Subgraph ◽  
Zero Divisor Graph ◽  
Ring Graph ◽  
Finite Commutative Rings

Let p be a prime number. Let G = Γ(R) be a ring graph, i.e. the zero-divisor graph of a commutative ring R. For an induced subgraph H of G, let CG(H) = {z ∈ V(G) ∣N(z) = V(H)}. Assume that in the graph G there exists an induced subgraph H which is isomorphic to the complete graph Kp-1, a vertex c ∈ CG(H), and a vertex z such that d(c, z) = 3. In this paper, we characterize the finite commutative rings R whose graphs G = Γ(R) have this property (called condition (Kp)).

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