The total domination stability of G, denoted by stγt (G), is the minimum size of a non-isolating set of vertices in G whose removal changes the total domination number. We prove that if G is a connected graph with maximum degree ∆ satisfying γt(G) ≥ 3, then stγt (G) ≤ 2∆ − 1.
Feb 19, 2018 · The total domination stability, st γ t ( G ) , of G is the minimum size of a non-isolating set of vertices in G whose removal changes the total ...
The total Roman domination stability number of a graph G with no isolated vertex, denoted by s t γ t R ( G ) , is the minimum number of vertices whose removal ...
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In this section we find the number of real roots of the total domination polynomial of some graphs. We are already find out total domination polynomials of ...
Abstract. For a graph G = (V,E), a subset D ⊆ V (G) is a dominating set if every vertex of V (G)\D has a neighbor in D. The domination number of G is the.
Jul 5, 2020 · We define the disjunctive total domination stability of G as the minimum size of a non-isolating set of vertices in G whose removal changes (increases or ...
Jul 6, 2016 · The domination stability, or just -stability, of a graph is the minimum number of vertices whose removal changes the domination number.
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The total domination stability, stt(G), of G is the minimum size of a non-isolating set of vertices in G whose removal changes the total domination number.
The purpose of this thesis is to study the effect that identifying or dotting two ver- tices has on the total domination number. We also study which graphs have ...
In this paper we present some bounds for the total Roman domination stability number of a graph, and prove that the associated decision problem is NP-hard even ...