Vertex-symmetric generalized Moore graphs

Symmetric Vertex Models on Planar Random Graphs

We discuss a 4-vertex model on an ensemble of 3-valent (Φ) planar random graphs, which has the effect of coupling the vertex model to 2D quantum gravity. The regular lattice equivalent of the model is the symmetric 8-vertex model on the honeycomb lattice, which can be mapped on to an Ising model in field, as was originally shown by Wu et.al. using generalised weak graph transformation technique...

Constructing vertex decomposable graphs

‎Recently‎, ‎some techniques such as adding whiskers and attaching graphs to vertices of a given graph‎, ‎have been proposed for constructing a new vertex decomposable graph‎. ‎In this paper‎, ‎we present a new method for constructing vertex decomposable graphs‎. ‎Then we use this construction to generalize the result due to Cook and Nagel‎.

Generalized Vertex Covering in Interval Graphs

Marathe, M.V., R. Ravi and C. Pandu Rangan, Generalized vertex covering in interval graphs. Discrete Applied Mathematics 39 (1992) 87-93. Given an integer i and an undirected graph G. the genera!ized i-verkx OFJPY pr&!z~ is to find a minimum set of vertices such that all chques in G of size i contain at least one vertex from this set. This problem is known to be NP-complete for chordal graphs w...

On Symmetric Moore Geometries

Generalized Symmetric Berwald Spaces

In this paper we study generalized symmetric Berwald spaces. We show that if a Berwald space $(M,F)$ admits a parallel $s-$structure then it is locally symmetric. For a complete Berwald space which admits a parallel s-structure we show that if the flag curvature of $(M,F)$ is everywhere nonzero, then $F$ is Riemannian.