Perfect secure domination in graphs | ||
| Categories and General Algebraic Structures with Applications | ||
| مقاله 9، دوره 7، Special Issue on the Occasion of Banaschewski's 90th Birthday (II) - شماره پیاپی 1، مهر 2017، صفحه 125-140 اصل مقاله (918.74 K) | ||
| نوع مقاله: Research Paper | ||
| نویسندگان | ||
| S.V. Divya Rashmi1؛ Subramanian Arumugam2؛ Kiran R. Bhutani3؛ Peter Gartland3 | ||
| 1Department of Mathematics, Vidyavardhaka College of Engineering, Mysuru 570002, Karnataka, India. | ||
| 2National Centre for Advanced Research in Discrete Mathematics, Kalasalingam University, Anand Nagar, Krishnankoil-626 126, Tamil Nadu, India. | ||
| 3Department of Mathematics, The Catholic University of America, Washington, D.C. 20064, USA. | ||
| چکیده | ||
| Let $G=(V,E)$ be a graph. A subset $S$ of $V$ is a dominating set of $G$ if every vertex in $V\setminus S$ is adjacent to a vertex in $S.$ A dominating set $S$ is called a secure dominating set if for each $v\in V\setminus S$ there exists $u\in S$ such that $v$ is adjacent to $u$ and $S_1=(S\setminus\{u\})\cup \{v\}$ is a dominating set. If further the vertex $u\in S$ is unique, then $S$ is called a perfect secure dominating set. The minimum cardinality of a perfect secure dominating set of $G$ is called the perfect secure domination number of $G$ and is denoted by $\gamma_{ps}(G).$ In this paper we initiate a study of this parameter and present several basic results. | ||
تازه های تحقیق | ||
Dedicated to Bernhard Banaschewski on the occasion of his 90th birthday | ||
| کلیدواژهها | ||
| Secure domination؛ perfect secure domination؛ secure domination number؛ perfect secure domination number | ||
| مراجع | ||
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