The maximal degree of a zero-divisor graph

Mohammad, Husam Q.; Shuker, Nazar H.; Khaleel, Luma A.

doi:10.1142/s179355712050151x

Cited by 2 publications

(2 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Since α � 5, p 1 � 3, and p 2 � 7, then (α/2) � 2 and |L 2 7 | � 3 2 − 3 � 6 so that μ(Γ(R)) � 8 : V 1 � 7.3 3 , 7.3 4 􏼈 􏼉, V 2 � 7.3 3 .2, 7.3 4 .2 􏼈 􏼉, V 3 � 7.3 3 .4 􏼈 􏼉, V 4 � 7.3 3…”

Section: □ Data Availabilitymentioning

confidence: 99%

See 1 more Smart Citation

The Metric Chromatic Number of Zero Divisor Graph of a Ring $Z_{n}$

Mohammad

Ibrahem

Khaleel

2022

International Journal of Mathematics and Mathematical Sciences

Self Cite

View full text Add to dashboard Cite

Let Γ be a nontrivial connected graph, c : V Γ ⟶ ℕ be a vertex colouring of Γ , and L i be the colouring classes that resulted, where i = 1,2 , … , k . A metric colour code for a vertex a of a graph Γ is c a = d a , L 1 , d a , L 2 , … , d a , L n , where d a , L i is the minimum distance between vertex a and vertex b in L i . If c a ≠ c b , for any adjacent vertices a and b of Γ , then c is called a metric colouring of Γ as well as the smallest number k satisfies this definition which is said to be the metric chromatic number of a graph Γ and symbolized μ Γ . In this work, we investigated a metric colouring of a graph Γ Z n and found the metric chromatic number of this graph, where Γ Z n is the zero-divisor graph of ring Z n .

show abstract

Section: □ Data Availabilitymentioning

confidence: 99%

“…After that, Anderson and Livingston modi ed this concept. From this time, many authors studied this graph and gave properties, see [3][4][5][6]. As well as, there are other studies on the zero divisor graph of ring integer modulo n, for example, see [7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%