Displaying similar documents to “The strong isometric dimension of finite reflexive graphs”

Statuses and double branch weights of quadrangular outerplanar graphs

Halina Bielak, Kamil Powroźnik (2015)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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In this paper we study some distance properties of outerplanar graphs with the Hamiltonian cycle whose all bounded faces are cycles isomorphic to the cycle C4. We call this family of graphs quadrangular outerplanar graphs. We give the lower and upper bound on the double branch weight and the status for this graphs. At the end of this paper we show some relations between median and double centroid in quadrangular outerplanar graphs.

Statuses and double branch weights of quadrangular outerplanar graphs

Halina Bielak, Kamil Powroźnik (2015)

Annales UMCS, Mathematica

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In this paper we study some distance properties of outerplanar graphs with the Hamiltonian cycle whose all bounded faces are cycles isomorphic to the cycle C4. We call this family of graphs quadrangular outerplanar graphs. We give the lower and upper bound on the double branch weight and the status for this graphs. At the end of this paper we show some relations between median and double centroid in quadrangular outerplanar graphs

On the strong metric dimension of the strong products of graphs

Dorota Kuziak, Ismael G. Yero, Juan A. Rodríguez-Velázquez (2015)

Open Mathematics

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Let G be a connected graph. A vertex w ∈ V.G/ strongly resolves two vertices u,v ∈ V.G/ if there exists some shortest u-w path containing v or some shortest v-w path containing u. A set S of vertices is a strong resolving set for G if every pair of vertices of G is strongly resolved by some vertex of S. The smallest cardinality of a strong resolving set for G is called the strong metric dimension of G. It is well known that the problem of computing this invariant is NP-hard. In this...

Small Ramsey numbers.

Radziszowski, Stanisław P. (1996)

The Electronic Journal of Combinatorics [electronic only]

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Two new classes of trees embeddable into hypercubes

Mounira Nekri, Abdelhafid Berrachedi (2010)

RAIRO - Operations Research

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The problem of embedding graphs into other graphs is much studied in the graph theory. In fact, much effort has been devoted to determining the conditions under which a graph G is a subgraph of a graph H, having a particular structure. An important class to study is the set of graphs which are embeddable into a hypercube. This importance results from the remarkable properties of the hypercube and its use in several domains, such as: the coding theory, transfer of information, multicriteria...

Asteroidal Quadruples in non Rooted Path Graphs

Marisa Gutierrez, Benjamin Lévêque, Silvia B. Tondato (2015)

Discussiones Mathematicae Graph Theory

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A directed path graph is the intersection graph of a family of directed subpaths of a directed tree. A rooted path graph is the intersection graph of a family of directed subpaths of a rooted tree. Rooted path graphs are directed path graphs. Several characterizations are known for directed path graphs: one by forbidden induced subgraphs and one by forbidden asteroids. It is an open problem to find such characterizations for rooted path graphs. For this purpose, we are studying in this...

Orientation distance graphs revisited

Wayne Goddard, Kiran Kanakadandi (2007)

Discussiones Mathematicae Graph Theory

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The orientation distance graph 𝓓ₒ(G) of a graph G is defined as the graph whose vertex set is the pair-wise non-isomorphic orientations of G, and two orientations are adjacent iff the reversal of one edge in one orientation produces the other. Orientation distance graphs was introduced by Chartrand et al. in 2001. We provide new results about orientation distance graphs and simpler proofs to existing results, especially with regards to the bipartiteness of orientation distance graphs...

Cycles in graphs and related problems

Antoni Marczyk

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Our aim is to survey results in graph theory centered around four themes: hamiltonian graphs, pancyclic graphs, cycles through vertices and the cycle structure in a graph. We focus on problems related to the closure result of Bondy and Chvátal, which is a common generalization of two fundamental theorems due to Dirac and Ore. We also describe a number of proof techniques in this domain. Aside from the closure operation we give some applications of Ramsey theory in the research of cycle...

The leafage of a chordal graph

In-Jen Lin, Terry A. McKee, Douglas B. West (1998)

Discussiones Mathematicae Graph Theory

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The leafage l(G) of a chordal graph G is the minimum number of leaves of a tree in which G has an intersection representation by subtrees. We obtain upper and lower bounds on l(G) and compute it on special classes. The maximum of l(G) on n-vertex graphs is n - lg n - 1/2 lg lg n + O(1). The proper leafage l*(G) is the minimum number of leaves when no subtree may contain another; we obtain upper and lower bounds on l*(G). Leafage equals proper leafage on claw-free chordal graphs. We use...

Computing the Metric Dimension of a Graph from Primary Subgraphs

Dorota Kuziak, Juan A. Rodríguez-Velázquez, Ismael G. Yero (2017)

Discussiones Mathematicae Graph Theory

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Let G be a connected graph. Given an ordered set W = {w1, . . . , wk} ⊆ V (G) and a vertex u ∈ V (G), the representation of u with respect to W is the ordered k-tuple (d(u, w1), d(u, w2), . . . , d(u, wk)), where d(u, wi) denotes the distance between u and wi. The set W is a metric generator for G if every two different vertices of G have distinct representations. A minimum cardinality metric generator is called a metric basis of G and its cardinality is called the metric dimension of...