Self-dual configurations and their Levi graphs

Self-dual Configurations and Regular Graphs

Self-dual graphs

We consider the three forms of self-duality that can be exhibited by a planar graph G, map self-duality, graph self-duality and matroid self-duality. We show how these concepts are related with each other and with the connectivity of G. We use the geometry of self-dual polyhedra together with the structure of the cycle matroid to construct all self-dual graphs. 1.1. Forms of Self-duality. Given...

Self-Dual Graphs

The study of self-duality has attracted some attention over the past decade. A good deal of research in that time has been done on constructing and classifying all self-dual graphs and in particular polyhedra. We will give an overview of the recent research in the first two chapters. In the third chapter, we will show the necessary condition that a self-complementary self-dual graph have n ≡ 0,...

Expansion Properties Of Levi Graphs

The Levi graph of a balanced incomplete block design is the bipartite graph whose vertices are the points and blocks of the design, with each block adjacent to those points it contains. We derive upper and lower bounds on the isoperimetric numbers of such graphs, with particular attention to the special cases of finite projective planes and Hadamard designs.

Configurations and Graphs

Cubic bipartite graphs with girth at least 6 correspond to symmetric combinatorial (v3) configurations. In 1887 V. Martinetti described a simple construction method which enables one to construct all combinatorial (v3) configurations from a set of so-called irreducible configurations. The result has been cited several times since its publication, both in the sense of configurations and graphs. ...