Complement graphs for zero-divisors of C (X)
Joint Authors
al-Afifi, Ghadah
Abu Usba, Imad
Source
Jordan Journal of Mathematics and Statistics
Issue
Vol. 7, Issue 3 (30 Sep. 2014), pp.185-205, 21 p.
Publisher
Yarmouk University Deanship of Research and Graduate Studies
Publication Date
2014-09-30
Country of Publication
Jordan
No. of Pages
21
Main Subjects
Abstract EN
Let X be a completely regular Hausdorff space and let C (X) be the ring of all continuous real valued functions defined on X.
The complement graph for the zero-divisors in C (X) is a simple graph in which two zero-divisor functions are adjacent if their product is non-zero.
In this article, the complement graph for the zero-divisor graph of C (X) and its line graph are studied.
It is shown that if X has more than 2 points, then these graphs are connected with radius 2, and diameter less than or equal to 3.
The girth is also calculated for them to be 3, and it is shown that they are always triangulated and hypertriangulated.
Bounds for the dominating number and clique number are also found for them in terms of the density number of X.
American Psychological Association (APA)
al-Afifi, Ghadah& Abu Usba, Imad. 2014. Complement graphs for zero-divisors of C (X). Jordan Journal of Mathematics and Statistics،Vol. 7, no. 3, pp.185-205.
https://search.emarefa.net/detail/BIM-414346
Modern Language Association (MLA)
al-Afifi, Ghadah& Abu Usba, Imad. Complement graphs for zero-divisors of C (X). Jordan Journal of Mathematics and Statistics Vol. 7, no. 3 (Sep. 2014), pp.185-205.
https://search.emarefa.net/detail/BIM-414346
American Medical Association (AMA)
al-Afifi, Ghadah& Abu Usba, Imad. Complement graphs for zero-divisors of C (X). Jordan Journal of Mathematics and Statistics. 2014. Vol. 7, no. 3, pp.185-205.
https://search.emarefa.net/detail/BIM-414346
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references : p. 204-205
Record ID
BIM-414346