On the outer-independent double Italian domination number
| Main Authors: | Abd Aziz, Noor A'lawiah; School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM Penang, Malaysia, Kamarulhaili, Hailiza; School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM Penang, Malaysia, Azvin, Farzaneh; Department of Mathematics, Shahed University, Tehran, Iran, Jafari Rad, Nader; Department of Mathematics, Shahed University, Tehran, Iran |
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| Format: | Article info application/pdf eJournal |
| Bahasa: | eng |
| Terbitan: |
GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB
, 2022
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| Subjects: | |
| Online Access: |
https://www.ejgta.org/index.php/ejgta/article/view/1346 https://www.ejgta.org/index.php/ejgta/article/view/1346/pdf_227 https://www.ejgta.org/index.php/ejgta/article/downloadSuppFile/1346/236 |
Daftar Isi:
- An outer-independent Italian dominating function (OIIDF) on a graph G is a function f : V(G)→{0, 1, 2} such that every vertex v ∈ V(G) with f(v)=0 has at least two neighbors assigned 1 under f or one neighbor w with f(w)=2, and the set {u ∈ V(G)|f(u)=0} is independent. An outer-independent double Italian dominating function (OIDIDF) on a graph G is a function f : V(G)→{0, 1, 2, 3} such that if f(v)∈{0, 1} for a vertex v ∈ V(G), then ∑u ∈ N[v]f(u)≥3 and the set {u ∈ V(G)|f(u)=0} is independent. The weight of an OIIDF (respectively, OIDIDF) f is the value w(f)=∑v ∈ V(G)f(v). The minimum weight of an OIIDF (respectively, OIDIDF) on a graph G is called the outer-independent Italian (respectively, outer-independent double Italian) domination number of G. We characterize all trees T with outer-independent double Italian domination number twice the outer-independent Italian domination number. We also present lower bounds on the outer-independent double Italian domination number of a connected graph G in terms of the order, minimum and maximum degrees.