Displaying similar documents to “A simple method for constructing small cubic graphs of girths 14, 15, and 16.”

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...

The irregularity of graphs under graph operations

Hosam Abdo, Darko Dimitrov (2014)

Discussiones Mathematicae Graph Theory

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The irregularity of a simple undirected graph G was defined by Albertson [5] as irr(G) = ∑uv∈E(G) |dG(u) − dG(v)|, where dG(u) denotes the degree of a vertex u ∈ V (G). In this paper we consider the irregularity of graphs under several graph operations including join, Cartesian product, direct product, strong product, corona product, lexicographic product, disjunction and sym- metric difference. We give exact expressions or (sharp) upper bounds on the irregularity of graphs under the...

L(2, 1)-Labelings of Some Families of Oriented Planar Graphs

Sagnik Sen (2014)

Discussiones Mathematicae Graph Theory

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In this paper we determine, or give lower and upper bounds on, the 2-dipath and oriented L(2, 1)-span of the family of planar graphs, planar graphs with girth 5, 11, 16, partial k-trees, outerplanar graphs and cacti.