All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 5 Next

Displaying 81 – 100 of 183

Showing per page

Metric dimension and zero forcing number of two families of line graphs

Linda Eroh, Cong X. Kang, Eunjeong Yi (2014)

Mathematica Bohemica

Zero forcing number has recently become an interesting graph parameter studied in its own right since its introduction by the “AIM Minimum Rank–Special Graphs Work Group”, whereas metric dimension is a well-known graph parameter. We investigate the metric dimension and the zero forcing number of some line graphs by first determining the metric dimension and the zero forcing number of the line graphs of wheel graphs and the bouquet of circles. We prove that Z ( G ) ≤ 2 Z ( L ( G ) ) for a simple and connected graph G . Further,...

Metric spaces with point character equal to their size

C. Avart, P. Komjath, Vojtěch Rödl (2010)

Commentationes Mathematicae Universitatis Carolinae

In this paper we consider the point character of metric spaces. This parameter which is a uniform version of dimension, was introduced in the context of uniform spaces in the late seventies by Jan Pelant, Cardinal reflections and point-character of uniformities, Seminar Uniform Spaces (Prague, 1973–1974), Math. Inst. Czech. Acad. Sci., Prague, 1975, pp. 149–158. Here we prove for each cardinal κ , the existence of a metric space of cardinality and point character κ . Since the point character can...

Metrically regular square of metrically regular bipartite graphs of diameter D = 7

Vladimír Vetchý (2018)

Archivum Mathematicum

The present paper deals with the spectra of powers of metrically regular graphs. We prove that there is only two tables of the parameters of an association scheme so that the corresponding metrically regular bipartite graph of diameter D = 7 (8 distinct eigenvalues of the adjacency matrix) has the metrically regular square. The results deal with the graphs of the diameter D < 7 see [8], [9] and [10].

Metrically regular square of metrically regular bipartite graphs of diameter D = 6

Vladimír Vetchý (1993)

Archivum Mathematicum

The present paper deals with the spectra of powers of metrically regular graphs. We prove that there is only one table of the parameters of an association scheme so that the corresponding metrically regular bipartite graph of diameter D = 6 (7 distinct eigenvalues of the adjacency matrix) has the metrically regular square. The results deal with the graphs of the diameter D < 6 see [7] and [8].

Minimal 2-dominating sets in trees

Marcin Krzywkowski (2013)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We provide an algorithm for listing all minimal 2-dominating sets of a tree of order n in time &#x1d4aa;(1.3248n). This implies that every tree has at most 1.3248n minimal 2-dominating sets. We also show that this bound is tight.

Minimal c p rank.

Shaked-Monderer, Naomi (2001)

ELA. The Electronic Journal of Linear Algebra [electronic only]

Minimal claw-free graphs

P. Dankelmann, Henda C. Swart, P. van den Berg, Wayne Goddard, M. D. Plummer (2008)

Czechoslovak Mathematical Journal

A graph G is a minimal claw-free graph (m.c.f. graph) if it contains no K 1 , 3 (claw) as an induced subgraph and if, for each edge e of G , G - e contains an induced claw. We investigate properties of m.c.f. graphs, establish sharp bounds on their orders and the degrees of their vertices, and characterize graphs which have m.c.f. line graphs.

Minimal forbidden subgraphs of reducible graph properties

Amelie J. Berger (2001)

Discussiones Mathematicae Graph Theory

A property of graphs is any class of graphs closed under isomorphism. Let ₁,₂,...,ₙ be properties of graphs. A graph G is (₁,₂,...,ₙ)-partitionable if the vertex set V(G) can be partitioned into n sets, V₁,V₂,..., Vₙ, such that for each i = 1,2,...,n, the graph G [ V i ] ∈ i . We write ₁∘₂∘...∘ₙ for the property of all graphs which have a (₁,₂,...,ₙ)-partition. An additive induced-hereditary property is called reducible if there exist additive induced-hereditary properties ₁ and ₂ such that = ₁∘₂. Otherwise...

Minimal rankings of the Cartesian product Kₙ ☐ Kₘ

Gilbert Eyabi, Jobby Jacob, Renu C. Laskar, Darren A. Narayan, Dan Pillone (2012)

Discussiones Mathematicae Graph Theory

For a graph G = (V, E), a function f:V(G) → 1,2, ...,k is a k-ranking if f(u) = f(v) implies that every u - v path contains a vertex w such that f(w) > f(u). A k-ranking is minimal if decreasing any label violates the definition of ranking. The arank number, ψ r ( G ) , of G is the maximum value of k such that G has a minimal k-ranking. We completely determine the arank number of the Cartesian product Kₙ ☐ Kₙ, and we investigate the arank number of Kₙ ☐ Kₘ where n > m.

Minimal reducible bounds for hom-properties of graphs

Amelie Berger, Izak Broere (1999)

Discussiones Mathematicae Graph Theory

Let H be a fixed finite graph and let → H be a hom-property, i.e. the set of all graphs admitting a homomorphism into H. We extend the definition of → H to include certain infinite graphs H and then describe the minimal reducible bounds for → H in the lattice of additive hereditary properties and in the lattice of hereditary properties.

Currently displaying 81 – 100 of 183