144,210 research outputs found
The center of an infinite graph
In this note we extend the notion of the center of a graph to infinite graphs. Thus, a vertex is in the center of the infinite graph G if it is in the center of an increasing family of finite subgraphs covering G. We give different characterizations of when a vertex is in the center of an infinite graph and we prove that any infinite graph with at least two ends has a center
Bis(μ-4-chloro-2-oxidobenzoato)bisÂ[(1,10-phenanthroline)copper(II)] dihydrate
The structure of the the title compound, [Cu2(C7H3ClO3)2(C12H8N2)2]·2H2O, consists of a dimeric unit involving a planar Cu2O2 group arranged around an inversion center. The coordination sphere of the CuII atom can be described as an elongated distorted square pyramid where the basal plane is formed by the two N atoms of the 1,10-phenanthroline molÂecule and the two O atoms of the hydroxyÂchloroÂbenzoate (hcbe) anion. The long apical Cu—O distance of 2.569 (2) Å involves the O atom of a symmetry-related hcbe anion, building up the dinuclear unit. Each dinuclear unit is connected through O—H⋯O hydrogen bonds involving two water molÂecules, resulting in an R
4
2(8) graph-set motif and building up an infinite chain parallel to (10). C—H⋯O interÂactions further stabilize the chain
Cubic Partial Cubes from Simplicial Arrangements
We show how to construct a cubic partial cube from any simplicial arrangement
of lines or pseudolines in the projective plane. As a consequence, we find nine
new infinite families of cubic partial cubes as well as many sporadic examples.Comment: 11 pages, 10 figure
- …