A new method for proving dominating uniqueness of graphs
Author
Source
Arab Journal of Basic and Applied Sciences
Issue
Vol. 24, Issue 0 (31 Oct. 2017), pp.292-299, 8 p.
Publisher
University of Bahrain College of Science
Publication Date
2017-10-31
Country of Publication
Bahrain
No. of Pages
8
Main Subjects
Natural & Life Sciences (Multidisciplinary)
Abstract EN
Let G be a graph of order n.
A subset S of VðGÞ is a dominating set of G if every vertex in VðGÞ n S is adjacent to at least one vertex of S.
The domination polynomial of G is the polynomial DðG; xÞ ¼ Pn i¼cðGÞ dðG; iÞxi, where dðG; iÞ is the number of dominating sets of G of size i, and cðGÞ is the size of a smallest dominating set of G, called the domination number of G.
We say two graphs G and H are dominating equivalent if DðG; xÞ ¼ DðH; xÞ.
A graph G is said to be dominating unique, or simply D-unique, if DðH; xÞ ¼ DðG; xÞ implies that H ffi G.
The goal of this paper is to find a new approach to determine the dominating uniqueness of graphs.
In this paper, we define a new graph polynomial, called star polynomial, and introduced an analogy notion of star uniqueness of graphs.
As an application, if G is a graph without isolated vertices, we show that a graph G is star unique if and only if G-Km is dominating unique for each m P 0.
As a by-product, the dominating uniqueness of many families of dense graphs is also determined.
American Psychological Association (APA)
Lau, Gee Choon. 2017. A new method for proving dominating uniqueness of graphs. Arab Journal of Basic and Applied Sciences،Vol. 24, no. 0, pp.292-299.
https://search.emarefa.net/detail/BIM-760676
Modern Language Association (MLA)
Lau, Gee Choon. A new method for proving dominating uniqueness of graphs. Arab Journal of Basic and Applied Sciences Vol. 24 (Oct. 2017), pp.292-299.
https://search.emarefa.net/detail/BIM-760676
American Medical Association (AMA)
Lau, Gee Choon. A new method for proving dominating uniqueness of graphs. Arab Journal of Basic and Applied Sciences. 2017. Vol. 24, no. 0, pp.292-299.
https://search.emarefa.net/detail/BIM-760676
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references : p. 299
Record ID
BIM-760676