Outer Independent Double Italian Domination of Some Graph Products

Authors

Rouhollah Jalaei, Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, IranFollow
Doost Ali Mojdeh, Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, IranFollow

Publication Date

February 2023

Abstract

An outer independent double Italian dominating function on a graph G is a function f:V(G) →{0,1,2,3} for which each vertex x ∈ V(G) with {f(x)∈ {0,1} then Σ_{y ∈ N[x]}f(y) ⩾ 3 and vertices assigned 0 under f are independent. The outer independent double Italian domination number γ_oidI(G) is the minimum weight of an outer independent double Italian dominating function of graph G. In this work, we present some contributions to the study of outer independent double Italian domination of three graph products. We characterize the Cartesian product, lexicographic product and direct product of custom graphs in terms of this parameter. We also provide the best possible upper and lower bounds for these three products for arbitrary graphs.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.

Recommended Citation

Jalaei, Rouhollah and Mojdeh, Doost Ali (2023) "Outer Independent Double Italian Domination of Some Graph Products," Theory and Applications of Graphs: Vol. 10: Iss. 1, Article 5.
DOI: 10.20429/tag.2023.100105
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol10/iss1/5