Displaying similar documents to “On the adjacent eccentric distance sum of graphs”

Extremely Irregular Graphs

M. Tavakoli, F. Rahbarnia, M. Mirzavaziri, A. R. Ashrafi, I. Gutman (2013)

Kragujevac Journal of Mathematics

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One-two descriptor of graphs

K. CH. Das, I. Gutman, D. Vukičević (2011)

Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques

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Two Short Proofs on Total Domination

Allan Bickle (2013)

Discussiones Mathematicae Graph Theory

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A set of vertices of a graph G is a total dominating set if each vertex of G is adjacent to a vertex in the set. The total domination number of a graph Υt (G) is the minimum size of a total dominating set. We provide a short proof of the result that Υt (G) ≤ 2/3n for connected graphs with n ≥ 3 and a short characterization of the extremal graphs.

γ-graphs of graphs

Gerd H. Fricke, Sandra M. Hedetniemi, Stephen T. Hedetniemi, Kevin R. Hutson (2011)

Discussiones Mathematicae Graph Theory

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A set S ⊆ V is a dominating set of a graph G = (V,E) if every vertex in V -S is adjacent to at least one vertex in S. The domination number γ(G) of G equals the minimum cardinality of a dominating set S in G; we say that such a set S is a γ-set. In this paper we consider the family of all γ-sets in a graph G and we define the γ-graph G(γ) = (V(γ), E(γ)) of G to be the graph whose vertices V(γ) correspond 1-to-1 with the γ-sets of G, and two γ-sets, say D₁ and D₂, are adjacent in E(γ)...

Further results on radial graphs

Kumarappan Kathiresan, G. Marimuthu (2010)

Discussiones Mathematicae Graph Theory

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In a graph G, the distance d(u,v) between a pair of vertices u and v is the length of a shortest path joining them. The eccentricity e(u) of a vertex u is the distance to a vertex farthest from u. The minimum eccentricity is called the radius of the graph and the maximum eccentricity is called the diameter of the graph. The radial graph R(G) based on G has the vertex set as in G, two vertices u and v are adjacent in R(G) if the distance between them in G is equal to the radius of G....

Graphs with equal domination and 2-distance domination numbers

Joanna Raczek (2011)

Discussiones Mathematicae Graph Theory

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Let G = (V,E) be a graph. The distance between two vertices u and v in a connected graph G is the length of the shortest (u-v) path in G. A set D ⊆ V(G) is a dominating set if every vertex of G is at distance at most 1 from an element of D. The domination number of G is the minimum cardinality of a dominating set of G. A set D ⊆ V(G) is a 2-distance dominating set if every vertex of G is at distance at most 2 from an element of D. The 2-distance domination number of G is the minimum...

The Distance Roman Domination Numbers of Graphs

Hamideh Aram, Sepideh Norouzian, Seyed Mahmoud Sheikholeslami (2013)

Discussiones Mathematicae Graph Theory

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Let k be a positive integer, and let G be a simple graph with vertex set V (G). A k-distance Roman dominating function on G is a labeling f : V (G) → {0, 1, 2} such that for every vertex with label 0, there is a vertex with label 2 at distance at most k from each other. The weight of a k-distance Roman dominating function f is the value w(f) =∑v∈V f(v). The k-distance Roman domination number of a graph G, denoted by γkR (D), equals the minimum weight of a k-distance Roman dominating...

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...