Displaying similar documents to “The Signed Total Roman k-Domatic Number Of A Graph”

Upper Bounds on the Signed Total (K, K)-Domatic Number of Graphs

Lutz Volkmann (2015)

Discussiones Mathematicae Graph Theory

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Let G be a graph with vertex set V (G), and let f : V (G) → {−1, 1} be a two-valued function. If k ≥ 1 is an integer and Σx∈N(v) f(x) ≥ k for each v ∈ V (G), where N(v) is the neighborhood of v, then f is a signed total k-dominating function on G. A set {f1, f2, . . . , fd} of distinct signed total k-dominating functions on G with the property that Σdi=1 fi(x) ≤ k for each x ∈ V (G), is called a signed total (k, k)-dominating family (of functions) on G. The maximum number of functions...

Total domination subdivision numbers of graphs

Teresa W. Haynes, Michael A. Henning, Lora S. Hopkins (2004)

Discussiones Mathematicae Graph Theory

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A set S of vertices in a graph G = (V,E) is a total dominating set of G if every vertex of V is adjacent to a vertex in S. The total domination number of G is the minimum cardinality of a total dominating set of G. The total domination subdivision number of G is the minimum number of edges that must be subdivided (where each edge in G can be subdivided at most once) in order to increase the total domination number. First we establish bounds on the total domination subdivision number...

Cubic Graphs with Total Domatic Number at Least Two

Saieed Akbari, Mohammad Motiei, Sahand Mozaffari, Sina Yazdanbod (2018)

Discussiones Mathematicae Graph Theory

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Let G be a graph with no isolated vertex. A total dominating set of G is a set S of vertices of G such that every vertex is adjacent to at least one vertex in S. The total domatic number of a graph is the maximum number of total dominating sets which partition the vertex set of G. In this paper we provide a criterion under which a cubic graph has total domatic number at least two.

A Note on Non-Dominating Set Partitions in Graphs

Wyatt J. Desormeaux, Teresa W. Haynes, Michael A. Henning (2016)

Discussiones Mathematicae Graph Theory

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A set S of vertices of a graph G is a dominating set if every vertex not in S is adjacent to a vertex of S and is a total dominating set if every vertex of G is adjacent to a vertex of S. The cardinality of a minimum dominating (total dominating) set of G is called the domination (total domination) number. A set that does not dominate (totally dominate) G is called a non-dominating (non-total dominating) set of G. A partition of the vertices of G into non-dominating (non-total dominating)...

Paired-domination

S. Fitzpatrick, B. Hartnell (1998)

Discussiones Mathematicae Graph Theory

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We are interested in dominating sets (of vertices) with the additional property that the vertices in the dominating set can be paired or matched via existing edges in the graph. This could model the situation of guards or police where each has a partner or backup. This paper will focus on those graphs in which the number of matched pairs of a minimum dominating set of this type equals the size of some maximal matching in the graph. In particular, we characterize the leafless graphs of...

The Domination Number of K 3 n

John Georges, Jianwei Lin, David Mauro (2014)

Discussiones Mathematicae Graph Theory

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Let K3n denote the Cartesian product Kn□Kn□Kn, where Kn is the complete graph on n vertices. We show that the domination number of K3n is [...]