scholarly journals Matching Number, Independence Number, and Covering Vertex Number of Γ(Zn)

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 49
Author(s):  
Eman AbuHijleh ◽  
Mohammad Abudayah ◽  
Omar Alomari ◽  
Hasan Al-Ezeh
Keyword(s):  
Zero Divisor ◽  
Independence Number ◽  
Independent Set ◽  
Covering Problem ◽  
Matching Number ◽  
Graph Invariants ◽  
Vertex Number ◽  
Zero Divisor Graph ◽  
Vertex Covering ◽  
Number Problem

Graph invariants are the properties of graphs that do not change under graph isomorphisms, the independent set decision problem, vertex covering problem, and matching number problem are known to be NP-Hard, and hence it is not believed that there are efficient algorithms for solving them. In this paper, the graph invariants matching number, vertex covering number, and independence number for the zero-divisor graph over the rings Z p k and Z p k q r are determined in terms of the sets S p i and S p i q j respectively. Accordingly, a formula in terms of p , q , k , and r, with n = p k , n = p k q r is provided.

scholarly journals On the Line Graph of the Zero Divisor Graph for the Ring of Gaussian Integers Modulo n

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Khalida Nazzal ◽  
Manal Ghanem
Keyword(s):  
Zero Divisor ◽  
Line Graph ◽  
Domination Number ◽  
The Other ◽  
Graph Invariants ◽  
Gaussian Integers ◽  
Zero Divisor Graph ◽  
Other Hand

Let Γ(ℤn[i]) be the zero divisor graph for the ring of the Gaussian integers modulo n. Several properties of the line graph of Γ(ℤn[i]), L(Γ(ℤn[i])) are studied. It is determined when L(Γ(ℤn[i])) is Eulerian, Hamiltonian, or planer. The girth, the diameter, the radius, and the chromatic and clique numbers of this graph are found. In addition, the domination number of L(Γ(ℤn[i])) is given when n is a power of a prime. On the other hand, several graph invariants for Γ(ℤn[i]) are also determined.

On enhanced power graphs of certain groups

2020 ◽  
pp. 2050099
Author(s):  
Sandeep Dalal ◽  
Jitender Kumar
Keyword(s):  
Cyclic Subgroup ◽  
Undirected Graph ◽  
Minimum Degree ◽  
Independence Number ◽  
Metric Dimension ◽  
Matching Number ◽  
Graph Invariants ◽  
Power Graph ◽  
Strong Metric Dimension ◽  
Vertex Set

The enhanced power graph [Formula: see text] of a group [Formula: see text] is a simple undirected graph with vertex set [Formula: see text] and two distinct vertices [Formula: see text] are adjacent if both [Formula: see text] and [Formula: see text] belongs to same cyclic subgroup of [Formula: see text]. In this paper, we obtain various graph invariants viz. independence number, minimum degree and matching number of [Formula: see text], where [Formula: see text] is the dicyclic group or a class of groups of order [Formula: see text]. If [Formula: see text] is any of these groups, we prove that [Formula: see text] is perfect and then obtain its strong metric dimension.

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

Roman domination and 2-independence in trees

2017 ◽  
Vol 09 (02) ◽  
pp. 1750023 ◽  
Author(s):  
Nacéra Meddah ◽  
Mustapha Chellali
Keyword(s):  
Independence Number ◽  
Minimum Weight ◽  
Domination Number ◽  
Independent Set ◽  
Maximum Cardinality ◽  
Roman Domination ◽  
Roman Domination Number ◽  
Number Formula ◽  
Sum Formula ◽  
Roman Dominating Function

A Roman dominating function (RDF) on a graph [Formula: see text] is a function [Formula: see text] satisfying the condition that every vertex [Formula: see text] with [Formula: see text] is adjacent to at least one vertex [Formula: see text] of [Formula: see text] for which [Formula: see text]. The weight of a RDF is the sum [Formula: see text], and the minimum weight of a RDF [Formula: see text] is the Roman domination number [Formula: see text]. A subset [Formula: see text] of [Formula: see text] is a [Formula: see text]-independent set of [Formula: see text] if every vertex of [Formula: see text] has at most one neighbor in [Formula: see text] The maximum cardinality of a [Formula: see text]-independent set of [Formula: see text] is the [Formula: see text]-independence number [Formula: see text] Both parameters are incomparable in general, however, we show that if [Formula: see text] is a tree, then [Formula: see text]. Moreover, all extremal trees attaining equality are characterized.

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

On the Adjacency Spectrum of Zero Divisor Graph of Ring ℤn

2021 ◽  
Author(s):  
Saraswati Bajaj ◽  
Pratima Panigrahi
Keyword(s):  
Zero Divisor ◽  
Zero Divisor Graph ◽  
Adjacency Spectrum

Independence Number and Covering Vertex Number of Γ(R(+)M)

2021 ◽  
Author(s):  
Manal Al-Labadi ◽  
Eman Mohammad Almuhur ◽  
Anwar Alboustanji
Keyword(s):  
Independence Number ◽  
Vertex Number
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