(G1,G2)-permutation graphs

Abstract

Let [Formula: see text] and [Formula: see text] be two labeled graphs of order [Formula: see text]. For any permutation [Formula: see text] the [Formula: see text]-permutation graph of labeled graphs [Formula: see text] and [Formula: see text] is the union of [Formula: see text] and [Formula: see text] together with the edges joining the vertex [Formula: see text] to the vertex [Formula: see text]. This operation on graphs is useful to produce a large class of networks with approximately the same properties as one of the original networks or even smaller. In this work we consider some properties of the permutation graph [Formula: see text], for labeled graph [Formula: see text] and [Formula: see text] of the same order. We provide bounds for the parameters radius, diameter, total distance, connectivity, edge-connectivity, chromatic number, and edge-chromatic number.