Results 11 to 20 of about 1,258,349 (257)

Weakly connected domination critical graphs [PDF]

Opuscula Mathematica, 2008
A dominating set \(D \subset V(G)\) is a weakly connected dominating set in \(G\) if the subgraph \(G[D]_w = (N_{G}[D],E_w)\) weakly induced by \(D\) is connected, where \(E_w\) is the set of all edges with at least one vertex in \(D\).
Magdalena Lemańska, Agnieszka Patyk
doaj   +3 more sources

Connected cototal domination number of a graph [PDF]

Transactions on Combinatorics, 2012
A dominating set $D subseteq V$ of a graph $G = (V,E)$ is said to be a connected cototal dominating set if $langle D rangle$ is connected and $langle V-D rangle neq phi$, contains no isolated vertices.
B Basavanagoud, Sunilkumar M Hosamani
doaj   +1 more source

Generalized connected domination in graphs [PDF]

Discrete Mathematics & Theoretical Computer Science, 2006
As a generalization of connected domination in a graph G we consider domination by sets having at most k components. The order γ c k (G) of such a smallest set we relate to γ c (G), the order of a smallest connected dominating set. For a tree
M. Kouider, P.D. Vestergaard
doaj   +2 more sources

Triple Connected Domination Number of a Graph [PDF]

, 2012
The concept of triple connected graphs with real life application was introduced by considering the existence of a path containing any three vertices of a graph G.
Selvam Avadayappan, T.Subramanian, Joseph, Paulraj, J.Paulraj Joseph, G.Mahadevan, Avadayappan, Selvam, Subramanian, T., Mahadevan, G.   +7 more
core   +1 more source

The Forcing Domination Number of Hamiltonian Cubic Graphs [PDF]

, 2009
The authors presented a sequence of Hamiltonian cubic graphs whose domination numbers are sharp and in this paper we study forcing domination number for those ...
H. Abdollahzadeh Ahangar, H.Abdollahzadeh Ahangar, Abdollahzadeh Ahangar, H., Pushpalatha L.   +3 more
core   +1 more source

Inequalities involving independence domination, $f$-domination, connected and total $f$-domination numbers [PDF]

, 2000
summary:Let $f$ be an integer-valued function defined on the vertex set $V(G)$ of a graph $G$. A subset $D$ of $V(G)$ is an $f$-dominating set if each vertex $x$ outside $D$ is adjacent to at least $f(x)$ vertices in $D$.
Wei, Bing, Muthammai, S., Zhou, Sanming, Janakiraman, T. N., Wang, Shaohui, Bhanumathi, M., Robert B. Allan, Renu Laskar   +7 more
core   +1 more source

Weakly connected domination subdivision numbers [PDF]

, 2008
A set D of vertices in a graph G = (V,E) is a weakly connected dominating set of G if D is dominating in G and the subgraph weakly induced by D is connected.
Raczek, Joanna
core   +1 more source

Outer-weakly convex domination number of graphs [PDF]

Communications in Combinatorics and Optimization, 2020
For a given simple graph $G=(V,E)$, a set $S\subseteq V$ is an outer-weakly convex dominating set if every vertex in $V\setminus S$ is adjacent to some vertex in $S$ and $V\setminus S$ is a weakly convex set.
Jonecis A. Dayap, Richard T. Alcantara, Roma M. Anoos   +2 more
doaj   +1 more source

Domination critical graphs [PDF]

, 1983
summary:A dominating set $D\subseteq V(G)$ is a {\it weakly connected dominating set} in $G$ if the subgraph $G[D]_w=(N_G[D],E_w)$ weakly induced by $D$ is connected, where $E_w$ is the set of all edges having at least one vertex in $D$.
Lemańska, Magdalena, Pattie Blitch, David P Sumner, Raczek, Joanna   +3 more
core   +1 more source

Structural Properties of Connected Domination Critical Graphs

Mathematics, 2021
A graph G is said to be k-γc-critical if the connected domination number γc(G) is equal to k and γc(G+uv)
Norah Almalki, Pawaton Kaemawichanurat
doaj   +1 more source