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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.

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 investigate natural extensions of the Continuous Image Graph (CIG) labelling scheme, which is based on the Consecutive Ones Property of matrices. The CIG labelling scheme generalizes tree labelling schemes to many graphs yet remaining as efficient, i.e., adjacency tests run in constant time, the space requirement is constant per node, and testing whether a graph is a CIG is possible in polyn...

An -labelling of a graph is an assignment of nonnegative integers to the vertices of such that the difference between the labels assigned to any two adjacent vertices is at least zero and the difference between the labels assigned to any two vertices which are at distance two is at least one. The span of an   0,1 L G G   0,1 L -labelling is the maximum label number assigned to any vertex of...

We prove that a binomial edge ideal of a graph G has a quadratic Gröbner basis with respect to some term order if and only if the graph G is closed with respect to a given labelling of the vertices. We also state some criteria for the closedness of a graph G that do not depend on the labelling of its vertex set.

A graph G is called a sum graph if there exists a labelling of the vertices of G by distinct positive integers such that the vertices labelled u and v are adjacent if and only if there exists a vertex labelled u + v. If G is not a sum graph, adding a nite number of isolated vertices to it will always yield a sum graph, and the sum number (G) of G is the smallest number of isolated vertices that...