The Italian Domination Numbers of Generalized Petersen Graphs P ( n,3)

Hong Gao, Changqing Xi, Kun Li, Qingfang Zhang and Yuansheng Yang
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Hong Gao: Department of Mathematics, Dalian Maritime University, Dalian 116026, China
Changqing Xi: Department of Mathematics, Dalian Maritime University, Dalian 116026, China
Kun Li: Department of Mathematics, Dalian Maritime University, Dalian 116026, China
Qingfang Zhang: Department of Mathematics, Dalian Maritime University, Dalian 116026, China
Yuansheng Yang: School of Computer Science and Technology, Dalian University of Technology, Dalian 116024, China

Mathematics, 2019, vol. 7, issue 8, 1-15

Abstract: An Italian dominating function of G is a function f : V ( G ) → { 0 , 1 , 2 } , for every vertex v such that f ( v ) = 0 , it holds that ∑ u ∈ N ( v ) f ( u ) ≥ 2 . The Italian domination number γ I ( G ) is the minimum weight of an Italian dominating function on G . In this paper, we determine the exact values of the Italian domination numbers of P ( n , 3 ) .

Keywords: Roman domination; Italian domination; generalized Petersen graphs (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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