Products of Geodesic Graphs and the Geodetic Number of Products

Jake A. Soloff; Rommy A. Márquez; Louis M. Friedler

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Displaying similar documents to “Products of Geodesic Graphs and the Geodetic Number of Products”

Explicit geodesic graphs on some H-type groups

Dušek, Zdeněk

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A homogeneous Riemannian manifold $M = G / H$ is called a “g.o. space” if every geodesic on $M$ arises as an orbit of a one-parameter subgroup of $G$ . Let $M = G / H$ be such a “g.o. space”, and $m$ an $Ad (H)$ -invariant vector subspace of $Lie (G)$ such that $Lie (G) = m \oplus Lie (H)$ . A is a map $ξ : m \to Lie (H)$ such that $t \mapsto exp (t (X + ξ (X))) (e H)$ is a geodesic for every $X \in m ∖ {0}$ . The author calculates explicitly such geodesic graphs for certain special 2-step nilpotent Lie groups. More precisely, he deals with “generalized Heisenberg groups” (also known as “H-type groups”) whose center has...

Generalized midset properties characterize geodesic circles and intervals

L. D. Loveland, J. E. Valentine (1978)

Colloquium Mathematicae

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Geodetic sets in graphs

Gary Chartrand, Frank Harary, Ping Zhang (2000)

Discussiones Mathematicae Graph Theory

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For two vertices u and v of a graph G, the closed interval I[u,v] consists of u, v, and all vertices lying in some u-v geodesic in G. If S is a set of vertices of G, then I[S] is the union of all sets I[u,v] for u, v ∈ S. If I[S] = V(G), then S is a geodetic set for G. The geodetic number g(G) is the minimum cardinality of a geodetic set. A set S of vertices in a graph G is uniform if the distance between every two distinct vertices of S is the same fixed number. A geodetic set is essential...

On properties of geodesic $η$ -preinvex functions.

Ahmad, I., Iqbal, Akhlad, Ali, Shahid (2009)

Advances in Operations Research

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On balls and totally geodesic submanifolds

P. G. Walczak (1984)

Annales Polonici Mathematici

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The hyperbolicity constant of infinite circulant graphs

José M. Rodríguez, José M. Sigarreta (2017)

Open Mathematics

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If X is a geodesic metric space and x1, x2, x3 ∈ X, a geodesic triangle T = {x1, x2, x3} is the union of the three geodesics [x1x2], [x2x3] and [x3x1] in X. The space X is δ-hyperbolic (in the Gromov sense) if any side of T is contained in a δ-neighborhood of the union of the two other sides, for every geodesic triangle T in X. Deciding whether or not a graph is hyperbolic is usually very difficult; therefore, it is interesting to find classes of graphs which are hyperbolic. A graph...

Some properties of geodesic semi E-b-vex functions

Adem Kiliçman, Wedad Saleh (2015)

Open Mathematics

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In this study, we introduce a new class of function called geodesic semi E-b-vex functions and generalized geodesic semi E-b-vex functions and discuss some of their properties.

Geodesic laminations with transverse Hölder distributions

Francis Bonahon (1997)

Annales scientifiques de l'École Normale Supérieure

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Geodesic graphs in Randers g.o. spaces

Zdeněk Dušek (2020)

Commentationes Mathematicae Universitatis Carolinae

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The concept of geodesic graph is generalized from Riemannian geometry to Finsler geometry, in particular to homogeneous Randers g.o. manifolds. On modified H-type groups which admit a Riemannian g.o. metric, invariant Randers g.o. metrics are determined and geodesic graphs in these Finsler g.o. manifolds are constructed. New structures of geodesic graphs are observed.