Jacobson, MS., J. Lehel and L.M. Lesniak, @threshold and $-tolerance chain graphs, Discrete Applied Mathematics 44 (1993) 191-203. In this paper we introduce a class of graphs called $-threshold graphs which generalize threshold graphs. These graphs are studied for various functions I+? that include “max” and “min” as special cases. The graphs are then shown to fit into the more general setting...

let $r$ be a commutative ring with identity. let $g(r)$ denote the maximal graph associated to $r$, i.e., $g(r)$ is a graph with vertices as the elements of $r$, where two distinct vertices $a$ and $b$ are adjacent if and only if there is a maximal ideal of $r$ containing both. let $gamma(r)$ denote the restriction of $g(r)$ to non-unit elements of $r$. in this paper we study the various graphi...