On a quasiordering of bipartite graphs.
In this note we extend results on the covering graphs of modular lattices (Zelinka) and semimodular lattices (Gedeonova, Duffus and Rival) to the covering graph of certain graded lattices.
An embedding of a simple graph G into its complement G̅ is a permutation σ on V(G) such that if an edge xy belongs to E(G), then σ(x)σ(y) does not belong to E(G). In this note we consider the embeddable (n,n)-graphs. We prove that with few exceptions the corresponding permutation may be chosen as cyclic one.
In 1986, Chartrand, Saba and Zou [3] defined a measure of the distance between (the isomorphism classes of) two graphs based on 'edge rotations'. Here, that measure and two related measures are explored. Various bounds, exact values for classes of graphs and relationships are proved, and the three measures are shown to be intimately linked to 'slowly-changing' parameters.