Bandwidth labelling is a well known research area in graph theory. We provide a new proof that the bandwidth of Mobius ladder is 4, if it is not a $K_{4}$, and investigate the bandwidth of a wider class of Mobius graphs of even strips.

We survey recent results on constructions of difference sets and strongly regular Cayley graphs by using union of cyclotomic classes of finite fields. Several open problems are raised.

We consider strongly regular graphs defined on a finite field by taking the union of some cyclotomic classes as difference set. Several new examples are found.

Let G be a family of n–vertex graphs of uniform degree 2 with the property that the union of any two member graphs has degree four. We determine the leading term in the asymptotics of the largest cardinality of such a family. Several analogous problems are discussed.

In this paper we introduce two new operations on graphs: sum and union corresponding to parallel and series operation respectively. We determine N-free graph as the graph that does not embed Necklace 4. We define “fin RelStr” as the set of all graphs with finite carriers. We also define the smallest class of graphs which contains the one-element graph and which is closed under parallel and seri...

A regular graph is superregular if it has no vertices or if the subgraphs induced by the neighbors and by the nonneighbors of each vertex are superreg-ular. The superregular graphs are precisely the disjoint union of m isomorphic cliques, the Cartesian product of two isomorphic cliques, the ve-cycle, and the complements of these graphs.

A join graph is the complete union of two arbitrary graphs. We give sufficient conditions for a join graph to be 1-factorizable. As a consequence of our results, the Hilton’s Overfull Subgraph Conjecture holds true for several subclasses of join graphs. © 2006 Elsevier B.V. All rights reserved.

In this paper we introduce two new operations on graphs: sum and union corresponding to parallel and series operation respectively. We determine N -free graph as the graph that does not embed Necklace 4. We define “fin RelStr” as the set of all graphs with finite carriers. We also define the smallest class of graphs which contains the one-element graph and which is closed under parallel and ser...

We begin the study of sets of near 1-factors of graphs G of odd order whose union contains all the edges of G and determine, for a few classes of graphs, the minimum number of near 1-factors in such sets. MSC 2000: Primary 05C70; Secondary 05C15.

We give a constructive characterization of graphs which are the union of k spanning trees after adding any new edge. This is a generalization of a theorem of Henneberg and Laman who gave the characterization for k = 2. We also give a constructive characterization of graphs which have k edgedisjoint spanning trees after deleting any edge of them.