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Completing graphs to metric spaces
[article]

2019
*
arXiv
*
pre-print

We prove that certain classes of

arXiv:1706.00295v3
fatcat:sfxputmtkve5xeg26qtkf5jwl4
*metrically*homogeneous*graphs*omitting triangles of odd short perimeter as well as triangles of long perimeter have the extension property for partial automorphisms and ... A*graph*G = (G, d) is*metric*if there exists a*metric**space*M = (G,d) such that d(u, v) =d(u, v) for every edge u, v of G. Such a*metric**space*M is also called a*metric**completion*of G. ... Knowing the characterisation of obstacles and a*completion*algorithm, it is then possible*to*turn such a*graph*into a*metric**space*in the given class. 1.4. ...##
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Completing graphs to metric spaces

2020

We prove that certain classes of

doi:10.11575/cdm.v16i2.71725
fatcat:6farfwb62jdu5jngjoekhg7age
*metrically*homogeneous*graphs*omitting triangles of odd short perimeter as well as triangles of long perimeter have the extension property for partial automorphisms and ... The eighth author would like*to*thank Jacob Rus for his Python style guidance. Similar results were also independently obtained by Rebecca Coulson and will appear in [5] . ... A*graph*G = (G, d) is*metric*if there exists a*metric**space*M = (G, d) such that d(u, v) = d(u, v) for every edge u, v of G. Such a*metric**space*M is also called a*metric**completion*of G. ...##
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On Quasi-Contractions in Metric Spaces with a Graph

2016
*
Hacettepe Journal of Mathematics and Statistics
*

Finally, we list some consequences of our theorem where either the contractive condition is replaced with a stronger one or the underlying

doi:10.15672/hjms.20164514282
fatcat:cdkwolzs4fg2bon2h2onoczwoq
*space*is changed*to*a*complete**metric**space*or a*complete*cone ...*metric**space*. ... Acknowledgments The authors are thankful*to*the Payame Noor University for supporting this research and also*to*the referee for his/her valuable comments*to*improve the paper. ...##
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α⁎-dominated set-valued mappings and some generalised fixed point results

2019
*
Journal of the National Science Foundation of Sri Lanka
*

Let be a

doi:10.4038/jnsfsr.v47i2.9165
fatcat:5ehdpxo6g5gyhgthlivledmz7q
*complete*dislocated b-*metric**space*endowed with a*graph*G. ... Let be a*complete*dislocated b-*metric**space*endowed with a*graph*G. ...##
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Page 930 of Mathematical Reviews Vol. , Issue 94b
[page]

1994
*
Mathematical Reviews
*

The following theorem provides conditions for the

*space*of*completed**graphs**to*be topologically*complete*. Let (X,d) be a sigma compact,*complete*, locally connected*metric**space*. ... Consequently, neither the*space*of bounded continuous functions nor the*space*of*completed**graphs*, equipped with the Hausdorff distance, is a*complete**metric**space*. ...##
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Linear openness of multifunctions in metric spaces

2005
*
International Journal of Mathematics and Mathematical Sciences
*

We discuss linear openness results for multifunctions with closed

doi:10.1155/ijmms.2005.203
fatcat:ii4aun5tsfbefdzj2amj5tamue
*graphs*in*metric**spaces*. ... Let the*metric**space*X be*complete*, and let the*metric**space*Y be*complete*and resemble normed*spaces*. Let the multifunction F have a closed*graph*. Let ω > 0 be a real number. ... Let the*metric**space*X be*complete*and let the*metric**space*Y resemble normed*spaces*. Let the multifunction F have a closed*graph*. Let ω > 0 be a real number. ...##
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Lexicographic metric spaces: basic properties and the metric dimension
[article]

2019
*
arXiv
*
pre-print

In this article, we introduce the concept of lexicographic

arXiv:1806.10908v2
fatcat:442m7f6xejdoljzyqtqdaq3fxu
*metric**space*and, after discussing some basic properties of these*metric**spaces*, such as*completeness*, boundedness, compactness and separability ... , we obtain a formula for the*metric*dimension of any lexicographic*metric**space*. ... Acknowledgements The author would like*to*thank his colleagues Douglas J. Klein, Cong X. Kang and Eunjeong Yi, who invited him*to*do a research stay at Texas A&M University in 2018. ...##
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Lexicographic metric spaces: Basic properties and the metric dimension

2020
*
Applicable Analysis and Discrete Mathematics
*

In this article, we introduce the concept of lexicographic

doi:10.2298/aadm180627004r
fatcat:7qylnwgbpva4nl52c7gwmojzsi
*metric**space*and, after discussing some basic properties of these*metric**spaces*, such as*completeness*, boundedness, compactness and separability ... , we obtain a formula for the*metric*dimension of any lexicographic*metric**space*. ... The author would like*to*thank his colleagues Douglas J. Klein, Cong X. Kang and Eunjeong Yi, who invited him*to*do a research stay at Texas A&M University in 2018. ...##
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Fixed point results for Hardy-Rogers type contractions with respect to a c-distance in graphical cone metric spaces

2020
*
Problemy Analiza
*

The aim of this paper is

doi:10.15393/j3.art.2020.6850
fatcat:ns7ecgybp5dkjaxxkfrzcdfe3q
*to*prove some existence and uniqueness results of the fixed points for Hardy-Rogers type contraction in cone*metric**spaces*associated with a -distance and endowed with a*graph*. ... instead of cone*metric**spaces*. ... The authors thank the Editorial Board and the referees for their valuable comments that helped*to*improve the text. ...##
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New examples of entire maximal graphs in H2×R1

2008
*
Differential geometry and its applications
*

The existence of these entire maximal

doi:10.1016/j.difgeo.2007.11.035
fatcat:zjl5oolisnfovfnh2vpfrdi67a
*graphs*shows that entire maximal*graphs*in this Lorentzian product*space*are not necessarily*complete*, on the contrary that in the Lorentz-Minkowski*space*. ... In this paper we obtain new explicit examples of*complete*and non-*complete*entire maximal*graphs*in H 2 × R 1 . ... Acknowledgement The author would like*to*heartily thank Luis J. Alías for some useful and valuable comments during the preparation of this work. ...##
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On minimum spanning tree-like metric spaces
[article]

2015
*
arXiv
*
pre-print

We attempt

arXiv:1505.06145v3
fatcat:xrkwxadv3fgqxohbtz4chpgrre
*to*shed new light on the notion of 'tree-like'*metric**spaces*by focusing on an approach that does not use the four-point condition. ... We prove that if a spanning tree representation, T, of M exists, then it is isomorphic*to*the unique minimum spanning tree in the weighted*complete**graph*associated with M, and we introduce a fourth-point ... Special thanks are extended*to*Yoshimasa Uematsu for his insights concerning the concept of median. ...##
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Fixed Point Theorems in Intuitionistic Fuzzy Graph Metric Space

2018
*
Annals of Pure and Applied Mathematics
*

fuzzy

doi:10.22457/apam.v17n1a7
fatcat:l7bywsdy55cfdnbcyz3x3z35gy
*graph**metric**space*are studied. ... In this paper, the contractive mapping on intuitionistic fuzzy*graph**metric**space*is discussed and the concepts of Lipschitz condition, ߳ −chain, contractive mapping, ߳ −contractive mapping on intuitionistic ... Authors would like*to*thank the editor and all the anonymous reviewers for their insightful comments and suggestions*to*improve this manuscript. ...##
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A finite Hausdorff dimension for graphs
[article]

2016
*
arXiv
*
pre-print

In this paper we apply this

arXiv:1607.08130v1
fatcat:edwgo3yairg7hkuie5xec5shbi
*to*connected simple*graphs*, a class that provides many interesting examples of finite*metric**spaces*. ...*metric**spaces*). ... The proof is*complete*. Theorem 8.6. A*metric**space*(F, d) is intrinsic iff there is an intrinsic*graph*G isometric*to*F . In other words, IG = I. Proof. ...##
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Расстояния Громова — Хаусдорфа до симплексов и некоторые приложения к дискретной оптимизации

2020
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Чебышевский сборник
*

Minimum Spanning Tree Problem Let be a

doi:10.22405/2226-8383-2020-21-2-169-189
fatcat:icjkbpcoyve7rpwsx47tbr2boq
*metric**space*. We consider as a weighted*complete**graph*( ) whose weight function equals*to*the distance between the corresponding edges. ... For a finite subset of a*metric**space*, consider the*complete**graph*( ) with the vertex set , endowed with the weight function whose value on an edge { , } equals*to*the distance | | between the points ...##
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Ultrametrics and complete multipartite graphs
[article]

2021
*
arXiv
*
pre-print

We describe the class of

arXiv:2103.09470v1
fatcat:wuffpg27zfdrdopoaq2pefdcze
*graphs*for which all*metric**spaces*with diametrical*graphs*belonging*to*this class are ultrametric. ... The bounded ultrametric*spaces*, which are weakly similar*to*unbounded ones, are also characterized via*complete*multipartite*graphs*. ... The purpose of the present paper is*to*show that*complete*multipartite*graphs*also provide an adequate description of ultrametric*spaces*in many cases. Let (X, d) be a*metric**space*. ...
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