Displaying similar documents to “Simple score sequences in oriented graphs.”

Notes on the independence number in the Cartesian product of graphs

G. Abay-Asmerom, R. Hammack, C.E. Larson, D.T. Taylor (2011)

Discussiones Mathematicae Graph Theory

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Every connected graph G with radius r(G) and independence number α(G) obeys α(G) ≥ r(G). Recently the graphs for which equality holds have been classified. Here we investigate the members of this class that are Cartesian products. We show that for non-trivial graphs G and H, α(G ☐ H) = r(G ☐ H) if and only if one factor is a complete graph on two vertices, and the other is a nontrivial complete graph. We also prove a new (polynomial computable) lower bound α(G ☐ H) ≥ 2r(G)r(H)...

Clique irreducibility of some iterative classes of graphs

Aparna Lakshmanan S., A. Vijayakumar (2008)

Discussiones Mathematicae Graph Theory

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In this paper, two notions, the clique irreducibility and clique vertex irreducibility are discussed. A graph G is clique irreducible if every clique in G of size at least two, has an edge which does not lie in any other clique of G and it is clique vertex irreducible if every clique in G has a vertex which does not lie in any other clique of G. It is proved that L(G) is clique irreducible if and only if every triangle in G has a vertex of degree two. The conditions for the iterations...

The niche graphs of interval orders

Jeongmi Park, Yoshio Sano (2014)

Discussiones Mathematicae Graph Theory

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The niche graph of a digraph D is the (simple undirected) graph which has the same vertex set as D and has an edge between two distinct vertices x and y if and only if N+D(x) ∩ N+D(y) ≠ ∅ or N−D(x) ∩ N−D(y) ≠ ∅, where N+D(x) (resp. N−D(x)) is the set of out-neighbors (resp. in-neighbors) of x in D. A digraph D = (V,A) is called a semiorder (or a unit interval order ) if there exist a real-valued function f : V → R on the set V and a positive real number δ ∈ R such that (x, y) ∈ A if...