2-arc closed subsets of graphs
by
Cheryl E. Praeger
University of Western Australia
Coauthors: Marston Conder, Margaret Morton

A subset S of vertices of a graph is said to be 2-arc closed if, whenever \alpha, \beta in S and a vertex \gamma is adjacent to both \alpha and \beta (that is, (\alpha, \beta, \gamma) is a 2-arc), then \gamma also belongs to S. The 2-arc closed subsets of most interest are those generated by a pair of vertices at distance at most 2 apart. These 2-arc closed subsets are usually called quads. A general discussion of the possible structure of quads is given followed by a description of some interesting examples of quads arising in partition graphs.

Date received: October 28, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cafp-06.