Displaying similar documents to “Requiring that Minimal Separators Induce Complete Multipartite Subgraphs”

A New Characterization of Unichord-Free Graphs

Terry A. McKee (2015)

Discussiones Mathematicae Graph Theory

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Unichord-free graphs are defined as having no cycle with a unique chord. They have appeared in several papers recently and are also characterized by minimal separators always inducing edgeless subgraphs (in contrast to characterizing chordal graphs by minimal separators always inducing complete subgraphs). A new characterization of unichord-free graphs corresponds to a suitable reformulation of the standard simplicial vertex characterization of chordal graphs.

The crossing numbers of join products of paths with graphs of order four

Marián Klešč, Stefan Schrötter (2011)

Discussiones Mathematicae Graph Theory

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Kulli and Muddebihal [V.R. Kulli, M.H. Muddebihal, Characterization of join graphs with crossing number zero, Far East J. Appl. Math. 5 (2001) 87-97] gave the characterization of all pairs of graphs which join product is planar graph. The crossing number cr(G) of a graph G is the minimal number of crossings over all drawings of G in the plane. There are only few results concerning crossing numbers of graphs obtained as join product of two graphs. In the paper, the exact values of crossing...

Graphs of low chordality.

Chandran, L.Sunil, Lozin, Vadim V., Subramanian, C.R. (2005)

Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]

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Isomorphic components of Kronecker product of bipartite graphs

Pranava K. Jha, Sandi Klavžar, Blaž Zmazek (1997)

Discussiones Mathematicae Graph Theory

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Weichsel (Proc. Amer. Math. Soc. 13 (1962) 47-52) proved that the Kronecker product of two connected bipartite graphs consists of two connected components. A condition on the factor graphs is presented which ensures that such components are isomorphic. It is demonstrated that several familiar and easily constructible graphs are amenable to that condition. A partial converse is proved for the above condition and it is conjectured that the converse is true in general.

Radio Graceful Hamming Graphs

Amanda Niedzialomski (2016)

Discussiones Mathematicae Graph Theory

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For k ∈ ℤ+ and G a simple, connected graph, a k-radio labeling f : V (G) → ℤ+ of G requires all pairs of distinct vertices u and v to satisfy |f(u) − f(v)| ≥ k + 1 − d(u, v). We consider k-radio labelings of G when k = diam(G). In this setting, f is injective; if f is also surjective onto {1, 2, . . . , |V (G)|}, then f is a consecutive radio labeling. Graphs that can be labeled with such a labeling are called radio graceful. In this paper, we give two results on the existence of radio...

On θ-graphs of partial cubes

Sandi Klavžar, Matjaz Kovse (2007)

Discussiones Mathematicae Graph Theory

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The Θ-graph Θ(G) of a partial cube G is the intersection graph of the equivalence classes of the Djoković-Winkler relation. Θ-graphs that are 2-connected, trees, or complete graphs are characterized. In particular, Θ(G) is complete if and only if G can be obtained from K₁ by a sequence of (newly introduced) dense expansions. Θ-graphs are also compared with familiar concepts of crossing graphs and τ-graphs.

A Characterization for 2-Self-Centered Graphs

Mohammad Hadi Shekarriz, Madjid Mirzavaziri, Kamyar Mirzavaziri (2018)

Discussiones Mathematicae Graph Theory

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A graph is called 2-self-centered if its diameter and radius both equal to 2. In this paper, we begin characterizing these graphs by characterizing edge-maximal 2-self-centered graphs via their complements. Then we split characterizing edge-minimal 2-self-centered graphs into two cases. First, we characterize edge-minimal 2-self-centered graphs without triangles by introducing specialized bi-independent covering (SBIC) and a structure named generalized complete bipartite graph (GCBG)....

Placing bipartite graphs of small size II

Beata Orchel (1996)

Discussiones Mathematicae Graph Theory

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In this paper we give all pairs of non mutually placeable (p,q)-bipartite graphs G and H such that 2 ≤ p ≤ q, e(H) ≤ p and e(G)+e(H) ≤ 2p+q-1.

The Least Eigenvalue of Graphs whose Complements Are Uni- cyclic

Yi Wang, Yi-Zheng Fan, Xiao-Xin Li, Fei-Fei Zhang (2015)

Discussiones Mathematicae Graph Theory

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A graph in a certain graph class is called minimizing if the least eigenvalue of its adjacency matrix attains the minimum among all graphs in that class. Bell et al. have identified a subclass within the connected graphs of order n and size m in which minimizing graphs belong (the complements of such graphs are either disconnected or contain a clique of size n/2 ). In this paper we discuss the minimizing graphs of a special class of graphs of order n whose complements are connected and...