May 29, 2023
Doost Ali Mojdeh

Doost Ali Mojdeh

Degree: Professor
Address: Department of Mathematics, University of Mazandaran, Babolsar, Iran
Education: Ph.D in Mathematics (Graph Theory and Combinatorics)
Phone: 011-35302448
Faculty: Faculty of Mathematical Sciences


Title On the Independent Double Roman Domination in Graphs
Type Article
Independent double Roman domination, Independent Roman {2}-domination, Independent domination, Graphs
Journal Bulletin of the Iranian Mathematical Society
Researchers Doost Ali Mojdeh (First researcher) , Zhila Mansouri (Second researcher)


An independent double Roman dominating function (IDRDF) on a graph G = (V, E) is a function f :V(G) → {0, 1, 2, 3} having the property that if f (v) = 0, then the vertex v has at least two neighbors assigned 2 under f or one neighbor w assigned 3 under f, and if f (v) = 1, then there exists w ∈ N(v) with f (w) ≥ 2, such that the set of vertices with positive weight is independent. The weight of an IDRDF is the valueu∈V f (u). The independent double Roman domination number idR(G) of a graph G is the minimum weight of an IDRDF on G. We continue the study of the independent double Roman domination and showits relationships to both independent domination number (IDN) and independent Roman {2}-domination number (IR2DN). We present several sharp bounds on the IDRDN of a graph G in terms of the order of G, maximum degree and the minimum size of edge cover. Finally, we show that, any ordered pair (a, b) is realizable as the IDN and IDRDN of some non-trivial tree if and only if 2a + 1 ≤ b ≤ 3a.