Academic Journal
Relations between the distinguishing number and some other graph parameters
| العنوان: | Relations between the distinguishing number and some other graph parameters |
|---|---|
| المؤلفون: | Bahman Ahmadi, Seyed Alireza Talebpour Shirazi Fard |
| المصدر: | ریاضی و جامعه, Vol 9, Iss 3, Pp 81-100 (2024) |
| بيانات النشر: | University of Isfahan, 2024. |
| سنة النشر: | 2024 |
| المجموعة: | LCC:Mathematics LCC:History of education |
| مصطلحات موضوعية: | graph, distinguishing number, independence number, line graph, Mathematics, QA1-939, History of education, LA5-2396 |
| الوصف: | A distinguishing coloring of a simple graph $G$ is a vertex coloring of $G$ which is preserved only by the identity automorphism of $G$. In other words, this coloring ``breaks'' all symmetries of $G$. The distinguishing number $D(G)$ of a graph $G$ is defined to be the smallest number of colors in a distinguishing coloring of $G$. This concept of “symmetry breaking” was first proposed by Babai in 1977 and after the publication of a seminal paper by Albertson in 1996, it attracted the attention of many mathematicians. In this paper, along with studying some relations between $D(G)$ and some other important graph parameters, we introduce the concept of a $(D,\alpha)$-ordinary graph which displays the comparison between $D(G)$ and the independence number $\alpha(G)$. Then we consider the classification of $(D,\alpha)$-ordinary graphs in various families of graphs such as forests, cycles, generalized Johnson graphs, Cartesian products of graphs and line graphs of connected claw-free graphs. We also propose some conjectures and discuss about some future research directions in this topic. |
| نوع الوثيقة: | article |
| وصف الملف: | electronic resource |
| اللغة: | Persian |
| تدمد: | 2345-6493 2345-6507 |
| Relation: | https://math-sci.ui.ac.ir/article_28265_6528a64072a5cef6776fc5d046eb8965.pdf; https://doaj.org/toc/2345-6493; https://doaj.org/toc/2345-6507 |
| DOI: | 10.22108/msci.2024.138274.1590 |
| URL الوصول: | https://doaj.org/article/205548f7aea54b6489dca553d2a9fda4 |
| رقم الانضمام: | edsdoj.205548f7aea54b6489dca553d2a9fda4 |
| قاعدة البيانات: | Directory of Open Access Journals |
| تدمد: | 23456493 23456507 |
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| DOI: | 10.22108/msci.2024.138274.1590 |