The Lattice Polynomial of a Graph

Jonathan Wiens1, Kara L. Nance1
1Department of Mathematical Sctences University of Alaska Fairbanks Fairbanks, AK 99775 USA

Abstract

This paper defines a new graph invariant by considering the set of connected induced subgraphs of a graph and defining a polynomial whose coefficients are determined by this partially ordered set of subgraphs. We compute the polynomial for a variety of graphs and also determine the effects on the polynomial of various graph operations.