Displaying similar documents to “Smallest cubic and quartic graphs with a given number of cutpoints and bridges.”

Characterization of block graphs with equal 2-domination number and domination number plus one

Adriana Hansberg, Lutz Volkmann (2007)

Discussiones Mathematicae Graph Theory

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Let G be a simple graph, and let p be a positive integer. A subset D ⊆ V(G) is a p-dominating set of the graph G, if every vertex v ∈ V(G)-D is adjacent with at least p vertices of D. The p-domination number γₚ(G) is the minimum cardinality among the p-dominating sets of G. Note that the 1-domination number γ₁(G) is the usual domination number γ(G). If G is a nontrivial connected block graph, then we show that γ₂(G) ≥ γ(G)+1, and we characterize all connected block...

Path and cycle factors of cubic bipartite graphs

M. Kano, Changwoo Lee, Kazuhiro Suzuki (2008)

Discussiones Mathematicae Graph Theory

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For a set S of connected graphs, a spanning subgraph F of a graph is called an S-factor if every component of F is isomorphic to a member of S. It was recently shown that every 2-connected cubic graph has a {Cₙ | n ≥ 4}-factor and a {Pₙ | n ≥ 6}-factor, where Cₙ and Pₙ denote the cycle and the path of order n, respectively (Kawarabayashi et al., J. Graph Theory, Vol. 39 (2002) 188-193). In this paper, we show that every connected cubic bipartite graph has a {Cₙ | n ≥ 6}-factor, and has...

Secure sets and their expansion in cubic graphs

Katarzyna Jesse-Józefczyk, Elżbieta Sidorowicz (2014)

Open Mathematics

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Consider a graph whose vertices play the role of members of the opposing groups. The edge between two vertices means that these vertices may defend or attack each other. At one time, any attacker may attack only one vertex. Similarly, any defender fights for itself or helps exactly one of its neighbours. If we have a set of defenders that can repel any attack, then we say that the set is secure. Moreover, it is strong if it is also prepared for a raid of one additional foe who can strike...

Characterizations of the Family of All Generalized Line Graphs-Finite and Infinite-and Classification of the Family of All Graphs Whose Least Eigenvalues ≥ −2

Gurusamy Rengasamy Vijayakumar (2013)

Discussiones Mathematicae Graph Theory

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The infimum of the least eigenvalues of all finite induced subgraphs of an infinite graph is defined to be its least eigenvalue. In [P.J. Cameron, J.M. Goethals, J.J. Seidel and E.E. Shult, Line graphs, root systems, and elliptic geometry, J. Algebra 43 (1976) 305-327], the class of all finite graphs whose least eigenvalues ≥ −2 has been classified: (1) If a (finite) graph is connected and its least eigenvalue is at least −2, then either it is a generalized line graph or it is represented...