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 ⊕ Lie ( H ) . A is a map ξ : m → Lie ( H ) such that t ↦ exp ( t ( X + ξ ( X ) ) ) ( e H ) is a geodesic for every X ∈ 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...

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...

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.