DOUBLY CONNECTED PITCHFORK DOMINATION AND IT'S INVERSE IN GRAPHS
Let G be a finite, simple, undirected graph and without isolated vertices. A subset D of V is a pitchfork dominating set if every vertex v G D dominates at least j and at most k vertices of V - D, for any j and k integers. A subset D~ of V - D is an inverse pitchfork dominating set if D~ is a domina...
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| Published in | TWMS journal of applied and engineering mathematics Vol. 12; no. 1; p. 82 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Istanbul
Turkic World Mathematical Society
01.01.2022
Elman Hasanoglu |
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| Online Access | Get full text |
| ISSN | 2146-1147 2146-1147 |
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| Abstract | Let G be a finite, simple, undirected graph and without isolated vertices. A subset D of V is a pitchfork dominating set if every vertex v G D dominates at least j and at most k vertices of V - D, for any j and k integers. A subset D~ of V - D is an inverse pitchfork dominating set if D~ is a dominating set. The domination number of G, denoted by [[gamma].sub.P]/(G) is a minimum cardinality over all pitchfork dominating sets in G. The inverse domination number of G, denoted by [Please download the PDF to view the mathematical expression] is a minimum cardinality over all inverse pitchfork dominating sets in G. In this paper, a special modified pitchfork dominations called doubly connected pitchfork domination and it's inverse are introduced when j = 1 and k = 2. Some properties and bounds are studied with respect to the order and the size of the graph. These modified dominations are applied and evaluated for several well known and complement graphs. Keywords: Dominating set, pitchfork domination, inverse pitchfork domination, doubly connected. AMS Subject Classification: 05C69 |
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| AbstractList | Let G be a finite, simple, undirected graph and without isolated vertices. A subset D of V is a pitchfork dominating set if every vertex v G D dominates at least j and at most k vertices of V - D, for any j and k integers. A subset D~ of V - D is an inverse pitchfork dominating set if D~ is a dominating set. The domination number of G, denoted by [[gamma].sub.P]/(G) is a minimum cardinality over all pitchfork dominating sets in G. The inverse domination number of G, denoted by [Please download the PDF to view the mathematical expression] is a minimum cardinality over all inverse pitchfork dominating sets in G. In this paper, a special modified pitchfork dominations called doubly connected pitchfork domination and it's inverse are introduced when j = 1 and k = 2. Some properties and bounds are studied with respect to the order and the size of the graph. These modified dominations are applied and evaluated for several well known and complement graphs. Keywords: Dominating set, pitchfork domination, inverse pitchfork domination, doubly connected. AMS Subject Classification: 05C69 Let G be a finite, simple, undirected graph and without isolated vertices. A subset D of V is a pitchfork dominating set if every vertex v G D dominates at least j and at most k vertices of V - D, for any j and k integers. A subset D~ of V - D is an inverse pitchfork dominating set if D~ is a dominating set. The domination number of G, denoted by [[gamma].sub.P]/(G) is a minimum cardinality over all pitchfork dominating sets in G. The inverse domination number of G, denoted by [Please download the PDF to view the mathematical expression] is a minimum cardinality over all inverse pitchfork dominating sets in G. In this paper, a special modified pitchfork dominations called doubly connected pitchfork domination and it's inverse are introduced when j = 1 and k = 2. Some properties and bounds are studied with respect to the order and the size of the graph. These modified dominations are applied and evaluated for several well known and complement graphs. Let G be a nite, simple, undirected graph and without isolated vertices. A subset D of V is a pitchfork dominating set if every vertex v 2 D dominates at least j and at most k vertices of V -D, for any j and k integers. A subset D-1 of V -D is an inverse pitchfork dominating set if D-1 is a dominating set. The domination number of G, denoted by pf (G) is a minimum cardinality over all pitchfork dominating sets in G. The inverse domination number of G, denoted by -1 pf (G) is a minimum cardinality over all inverse pitchfork dominating sets in G. In this paper, a special modi ed pitchfork dominations called doubly connected pitchfork domination and it's inverse are introduced when j = 1 and k = 2. Some properties and bounds are studied with respect to the order and the size of the graph. These modi ed dominations are applied and evaluated for several well known and complement graphs. |
| Audience | Academic |
| Author | Al-Harere, M. N Abdlhusein, M. A |
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| Copyright | COPYRIGHT 2022 Turkic World Mathematical Society 2022. This work is licensed under http://creativecommons.org/licenses/by-nc/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License. |
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| Snippet | Let G be a finite, simple, undirected graph and without isolated vertices. A subset D of V is a pitchfork dominating set if every vertex v G D dominates at... Let G be a nite, simple, undirected graph and without isolated vertices. A subset D of V is a pitchfork dominating set if every vertex v 2 D dominates at least... |
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| StartPage | 82 |
| SubjectTerms | Apexes Graph theory Graphs Mathematical research Mathematics |
| Title | DOUBLY CONNECTED PITCHFORK DOMINATION AND IT'S INVERSE IN GRAPHS |
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