DOUBLY CONNECTED PITCHFORK DOMINATION AND IT'S INVERSE IN GRAPHS

• Published in: TWMS journal of applied and engineering mathematics Vol. 12; no. 1; p. 82
• Main Authors: Abdlhusein, M. A, Al-Harere, M. N
• Format: Journal Article
• Language: English
• Published: Istanbul Turkic World Mathematical Society 01.01.2022; Elman Hasanoglu
• Subjects: Apexes; Graph theory; Graphs; Mathematical research; Mathematics; Iraq
• ISSN: 2146-1147; 2146-1147

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