Last edited by Yozshujinn

Friday, May 8, 2020 | History

2 edition of **Minimal hereditary dominating pair graphs.** found in the catalog.

Minimal hereditary dominating pair graphs.

NataЕЎa PrЕѕulj

- 315 Want to read
- 15 Currently reading

Published
**2000**
by University of Toronto, Dept. of Computer Science in Toronto
.

Written in English

The Physical Object | |
---|---|

Pagination | 67 leaves. |

Number of Pages | 67 |

ID Numbers | |

Open Library | OL19895861M |

ISBN 10 | 0612503658 |

In the special case of graphs of independence number 𝛼 = 3 without induced chordless cycles 7 it is shown that exists connected dominating set of vertices with number of vertices () ≤4. Using the concept of connected dominating sets, we defined a new invariant ℎ() that does not exceed the number of : Vladimir Bercov. If the alleles of an inherited pair differ, then one determines the organisms appearance and is called the Dominant allele. The other has no noticeable effect on the organisms appearance and is the Recessive Allele.

It was previously known [18] that °(G £ H) • 4°(G)°(H) for every pair of graphs G and H. If S is any dominating set for a graph G, then S is a subset of a total dominating set for G. Consider the vertices of S sequentially and enlarge the set to include a neighbor of any x 2 S that is isolated in the subgraph induced by S. The. This book supplements the textbook of the authors" Lectures on Graph The ory" [6] by more than thousand exercises of varying complexity. The books match each other in their contents, notations, and terminology. The authors hope that both students and lecturers will find this book helpful for mastering and verifying the understanding of the peculiarities of s: 1.

The book is self-contained, and is suitable for both reference and learning, with many chapters containing exercises and solutions to seleced problems. It will be valuable for researchers and graduate and advanced undergraduate students in discrete mathematics and theoretical computer science, in particular those engaged with graph theory and. Wednesday, April 20 th, at am NS F Finding detours and Gallai vertices in distance-hereditary graphs Professor André Kézdy University of Louisville Abstract: A detour of a graph is a path of maximum length. A vertex that is common to .

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An asteroidal triple (AT) is a set of vertices such that each pair of vertices is joined by a path that avoids the neighborhood of the third.

Every AT-free graph contains a dominating pair, a pair of vertices such that for every path between them, every vertex of the graph is within distance one of the say that a graph is a hereditary dominating pair (HDP) graph if each of its Cited by: 5.

For example, the maximum number of minimal dominating sets in graphs is known to be at most n, however no graph having more than n minimal dominating sets is known.

On the other hand, on many graph classes matching upper and lower bounds can be shown on the maximum number of minimal dominating sets [8], [10].Cited by: 8. An independent set of three vertices is called an asteroidal triple if between each pair in the triple there exists a path that avoids the neighborhood of the third.

A graph is asteroidal triple-free (AT-free) if it contains no asteroidal triple. The motivation for this investigation is provided, in part, by the fact that AT-free graphs offer a common generalization of interval, permutation Cited by: the minimum r-dominating clique problem on distance-hereditary graphs these kinds of vertices turn out to be of importance.

Lemma I ([9]) Let x be a leaf in graph G and let y be its neighbor. Enumerating minimal connected dominating sets in graphs of bounded chordalityI,II Petr A. Golovacha, Pinar Heggernesa, Dieter Kratschb aDepartment of Informatics, University of Bergen, N Bergen, Norway bUniversite de Lorraine, LITA, Metz, France´ Abstract Enumerating objects of speciﬁed type is one of the principal tasks in algorithmics.

The minimal dominating graph MD(G) of G is the intersection graph defined on the family of all minimal dominating sets of vertices in G. This concept was introduced by. Przulj, Minimal Minimal hereditary dominating pair graphs. book Dominating Pair Graphs, Thesis, Graduate Department of Computer Science, University of Toronto, January Press Coverage Health: Learning from big data how life works, Interview ERC grantee Natasa Przulj, Professor of Biomedical Data Science at UCL, The European Research Council Magazine, Septem A graph may have many MISs of widely varying sizes; the largest, or possibly several equally large, MISs of a graph is called a maximum independent graphs in which all maximal independent sets have the same size are called well-covered graphs.

The phrase "maximal independent set" is also used to describe maximal subsets of independent elements in. dominating set, that is a paired-dominating set that forms an induced match-ing, and that such set can be chosen to be a minimum paired-dominating set.

We use these results to obtain a new characterization of {E, net, C5}-free graphs in terms of the hereditary existence of induced paired-dominating sets. In graph theory, a branch of discrete mathematics, a distance-hereditary graph (also called a completely separable graph) is a graph in which the distances in any connected induced subgraph are the same as they are in the original graph.

Thus, any induced subgraph inherits the distances of the larger graph. Distance-hereditary graphs were named and first studied by Howorka.

A graph G is frame hereditary dominating pair (frame HDP Hereditary dominating pair graphs. Discrete Appl.

Math. No, () Related classes. The map shows the inclusions between the current class and a fixed set of landmark classes.

Minimal/maximal is with respect to the contents of ISGCI. Only references for direct. Abstract. A graph is distance-hereditary if and only if each cycle on five or more vertices has at least two crossing chords.

We present linear time algorithms for the minimum r-dominating clique and maximum strict r-packing set problems on distance-hereditary related problems such as diameter, radius, central vertex, r-dominating by Cited by: An Algorithm for Minimal and Minimum Distance - 2 Dominating Sets of Graph Apart from chess, domination in graphs has applications to several other fields.

There are more than a hundred models of dominating and related types of sets in A dominating set D is called a minimal dominating set if no proper subset of D is a dominating set. cuit in G of length at least 5 has a pair of chords that cross each other.

Evidently every distance-hereditary graph is weakly chordal. We show that the condition for the existence of r-dominating cliques known from [9] on Helly graphs and chordal graphs is still valid in the case of distance-hereditary graphs.

Also we give. Minimal/maximal is with respect to the contents of ISGCI. Only references for direct inclusions are given. Unbounded from book thickness Unbounded from pathwidth Unbounded from chromatic number Hereditary dominating pair graphs.

Discrete Appl. Math.No, () Weighted problems. total dominating or an independent dominating set. 2 A pair of disjoint dominating and total dom-inating sets The authors in [15, 17, 18] have determined certain conditions under which a graph Ghas a vertex set V(G) having a pair of subsets consisting of a dominating set and a total dominating set which are disjoint.

Mathematical Model by Fuzzy Rules from Dominating Graphs Author: Dr. Nirmala, Mr. Dhanabal Subject: International Journal of Scientific and Research Publications, Volume 3, Issue 2, February • γP(G) is the minimum cardinality of a dominating set that is a P-set; • βP(G) is the maximum cardinality of a P-set; • iP(G) is the minimum cardinality of a maximal P-set; • ΓP(G) is the maximum cardinality of a minimal dominating set that is a P-set.

The generalized independence number βP(G) has been studied before (for example in [2]) with various notations. Abstract. In this work we introduce graphs with bounded induced distance of order k (BID(k) for short).In any graph belonging to BID(k), the length of every induced path between every pair of nodes is at most k times the distance between the same communication networks modeled by these graphs any message can be always delivered through a path whose length Cited by: A Review on Graphs with Unique Minimum Dominating Sets 1 izhi 2 V Revathi 1Research Scholar, Sakthi College of Arts and Science For Women, Oddanchatram.

2Assistant Professor, Department of Mathematics, Sakthi College of Arts and Science For Women, Oddanchatram. ABSTRACT – A dominating set for a graph G is a. On Subdivision Graphs which are 2-steps Hyperhamiltonian Graphs and Hereditary Nonsteps Hamiltonian Graphs.

Reconstruction of Graphs from Dominating Sets. Minimal Tile and Bond-Edge Types for Self-Assembling DNA Graphs of Triangular Tiles.subsequent discussion, we generalize this result and characterize k-chordal graphs based on their minimal vertex separators.

We use terms minimal vertex separators and minimal (a,b)-vertex separators interchangeably and the pair (a,b) under consideration will be clear from the context. Theorem 9. Let k ≥ 3 be an integer.Paired- and inducedpaired-dominationin (E,net)-freegraphs 3 75 [10] and later by Zelinka [11].

They are also studied (as dominating induced 76 matchings) by Telle [9]. 77 The complete bipartite graph K1,3 is often called the claw. The graph 78 E is obtained from the claw by subdividing two of its three edges exactly 79 once. The graph net is obtained by attaching a .