ANNIHILATOR DOMINATION NUMBER OF TENSOR PRODUCT OF PATH GRAPHS

• Published in: TWMS journal of applied and engineering mathematics Vol. 9; no. 4; p. 800
• Main Authors: Sharma, K, Sharma, U
• Format: Journal Article
• Language: English
• Published: Istanbul Turkic World Mathematical Society 01.01.2019; Elman Hasanoglu
• Subjects: Advertising executives; Apexes; Graph theory; Graphs; Mathematical analysis; Tensors; Upper bounds; India
• ISSN: 2146-1147; 2146-1147

An annihilator dominating set (ADS) is a representative technique for finding the induced subgraph of a graph which can help to isolate the vertices. A dominating set of graph G is called ADS if its induced subgraph is containing only isolated vertices. The annihilator domination number of G, denoted by [[gamma].sub.[alpha]](G) is the minimum cardinality of ADS. The tensor product of graphs G and H signified by G x H is a graph with vertex set V = V(G) x V(H) and edge {(u,v), (u', v')} [member of] E whenever (u,u') [member of] E(G) and (v, v') [member of] E(H). In this paper, we deduce exact values of annihilator domination number of tensor product of [P.sub.m] and [P.sub.n], m,n [greater than or equal to] 2. Further, we investigated some lower and upper bounds for annihilator domination number of tensor product of path graphs. Keywords: Domination Number, Annihilator Dominating Set, Annihilator Domination Number, Paths, Tensor Product. AMS Subject Classification: 05C69, 05C50, 05C76