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### Completing graphs to metric spaces [article]

Andrés Aranda, David Bradley-Williams, Eng Keat Hng, Jan Hubička, Miltiadis Karamanlis, Michael Kompatscher, Matěj Konečný, Micheal Pawliuk
2019 arXiv   pre-print
We prove that certain classes of 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.  ...

### Completing graphs to metric spaces

Andres Aranda, David Bradley-Williams, Eng Keat Hng, Jan Hubička, Miltiadis Karamanlis, Michael Kompatscher, Matěj Konečný, Micheal Pawliuk
2020
We prove that certain classes of 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  .  ...  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.  ...

### On Quasi-Contractions in Metric Spaces with a Graph

Kamal Fallahi
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 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.  ...

### α⁎-dominated set-valued mappings and some generalised fixed point results

2019 Journal of the National Science Foundation of Sri Lanka
Let be a complete dislocated b-metric space endowed with a graph G.  ...  Let be a complete dislocated b-metric space endowed with a graph G.  ...

### 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.  ...

### Linear openness of multifunctions in metric spaces

Corneliu Ursescu
2005 International Journal of Mathematics and Mathematical Sciences
We discuss linear openness results for multifunctions with closed 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.  ...

### Lexicographic metric spaces: basic properties and the metric dimension [article]

Juan Alberto Rodriguez-Velazquez
2019 arXiv   pre-print
In this article, we introduce the concept of lexicographic 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.  ...

### Lexicographic metric spaces: Basic properties and the metric dimension

Juan Rodriuez-Velazquez
2020 Applicable Analysis and Discrete Mathematics
In this article, we introduce the concept of lexicographic 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.  ...

### Fixed point results for Hardy-Rogers type contractions with respect to a c-distance in graphical cone metric spaces

L. Aryanpour, H. Rahimi, G. Soleimani Rad
2020 Problemy Analiza
The aim of this paper is 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.  ...

### New examples of entire maximal graphs in H2×R1

Alma L. Albujer
2008 Differential geometry and its applications
The existence of these entire maximal 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.  ...

### On minimum spanning tree-like metric spaces [article]

Momoko Hayamizu, Kenji Fukumizu
2015 arXiv   pre-print
We attempt 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.  ...

### Fixed Point Theorems in Intuitionistic Fuzzy Graph Metric Space

S.Yahya Mohamed, Govt. Arts College, Trichy, A.Mohamed Ali
2018 Annals of Pure and Applied Mathematics
fuzzy 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.  ...

### A finite Hausdorff dimension for graphs [article]

Juan M. Alonso
2016 arXiv   pre-print
In this paper we apply this 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.  ...

### Расстояния Громова — Хаусдорфа до симплексов и некоторые приложения к дискретной оптимизации

Александр Олегович Иванов, Алексей Августинович Тужилин
2020 Чебышевский сборник
Minimum Spanning Tree Problem Let be a 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  ...

### Ultrametrics and complete multipartite graphs [article]

Viktoriia Bilet, Oleksiy Dovgoshey, Yuriy Kononov
2021 arXiv   pre-print
We describe the class of 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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