New results on ptolemaic graphs

Markenzon, Lilian; Waga, Christina Fraga Esteves Maciel

doi:10.1016/j.dam.2014.03.024

Cited by 11 publications

(5 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A strictly chordal graph is obtained by adding zero or more true twins to each vertex of a block graph G. A new characterization based on minimal vertex separators was presented by Markenzon and Waga [21]. Based on the characterization theorem, a recognition algorithm becomes very simple.…”

Section: Chordal and Strictly Chordal Graphsmentioning

confidence: 99%

Integer Laplacian eigenvalues of chordal graphs

Abreu

Justel

Markenzon

2021

Linear Algebra and its Applications

Self Cite

View full text Add to dashboard Cite

In this paper, we establish the relation between classic invariants of graphs and their integer Laplacian eigenvalues, focusing on a subclass of chordal graphs, the strictly chordal graphs, and pointing out how their computation can be efficiently implemented. Firstly we review results concerning general graphs showing that the number of universal vertices and the degree of false and true twins provide integer Laplacian eigenvalues and their multiplicities. Afterwards, we prove that many integer Laplacian eigenvalues of a strictly chordal graph are directly related to particular simplicial vertex sets and to the minimal vertex separators of the graph.

show abstract

Section: Chordal and Strictly Chordal Graphsmentioning

confidence: 99%

Integer Laplacian eigenvalues of chordal graphs

Abreu

Justel

Markenzon

2021

Linear Algebra and its Applications

Self Cite

View full text Add to dashboard Cite

show abstract

“…Brandstädt and Wagner [9] showed that the class is the same as the (4, 6)-leaf power graphs. Strictly chordal graphs can also be characterized in terms of the structure of their separators [30]. Some known subclasses of strictly chordal graphs are: block graphs [19], AC-graphs [6], 3-leaf power graphs [15,8], strictly interval graphs [31] and generalized core-satellite graphs [16].…”

Section: Introductionmentioning

confidence: 99%

Linear time determination of the scattering number for strictly chordal graphs

Markenzon¹,

Waga²

2021

Preprint

Self Cite

View full text Add to dashboard Cite

The scattering number of a graph G was defined by Jung in 1978 as scis the number of connected components of the graph G − S. It is a measure of vulnerability of a graph and it has a direct relationship with the toughness of a graph. Strictly chordal graphs, also known as block duplicate graphs, are a subclass of chordal graphs that includes block and 3-leaf power graphs. In this paper we present a linear time solution for the determination of the scattering number and scattering set of strictly chordal graphs. We show that, although the knowledge of the toughness of the class is helpful, it is not sufficient to provide an immediate result for determining the scattering number.

show abstract

“…The class was later defined as strictly chordal graphs by Kennedy (2005) based on hypergraph properties. A new characterization based on minimal vertex separators was presented by Markenzon and Waga (). In this paper, we continue to study properties of maximal cliques and minimal vertex separators, presenting a linear time determination of the toughness of strictly chordal graphs.…”

Section: Introductionmentioning

confidence: 99%

“…Based on the theorem, the recognition algorithm becomes trivial. Theorem (Markenzon and Waga, ) . Let

G = (V, E)

be a chordal graph and

double-struckS

be the set of minimal vertex separators of G .…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Toughness and Hamiltonicity of strictly chordal graphs

Markenzon

Waga

2016

Int Trans Operational Res

Self Cite

View full text Add to dashboard Cite

The clique‐based structure of chordal graphs allows the development of efficient solutions for many algorithmic problems. In this context, the minimal vertex separators play a decisive role. In this paper, we study properties of these structures, presenting a linear time determination of the toughness of strictly chordal graphs. We prove that every 1‐tough strictly chordal graph is Hamiltonian. This result leads to the characterization of a new class, the Hamiltonian strictly chordal graphs. We also prove that graphs belonging to this class are cycle extendable.

show abstract

New results on ptolemaic graphs

Cited by 11 publications

References 9 publications

Integer Laplacian eigenvalues of chordal graphs

Integer Laplacian eigenvalues of chordal graphs

Linear time determination of the scattering number for strictly chordal graphs

Toughness and Hamiltonicity of strictly chordal graphs

Contact Info

Product

Resources

About