Skolem labellings of generalised Dutch windmills

Skolem-labeling of generalized three-vane windmills

A graph on 2n vertices can be Skolem-labeled if the vertices can be given labels from {1, . . . , n} such that each label i is assigned to exactly two vertices and these vertices are at distance i. Mendelsohn and Shalaby have characterized the Skolem-labeled paths, cycles and windmills (of fixed vane length). In this paper, we obtain necessary conditions for the Skolem-labeling of generalized k...

Skolem arrays and skolem labellings of ladder graphs

Skolem Sequences and Erdosian Labellings of m Paths with 2 and 3 Vertices

Assume that we have m identical graphs where the graphs consists of paths with k vertices where k is a positive integer. In this paper, we discuss certain labelling of the m graphs called c-Erdösian for some positive integers c. We regard labellings of the vertices of the graphs by positive integers, which induce the edge labels for the paths as the sum of the two incident vertex labels. They h...

A new infinite family of graceful generalised Petersen graphs, via graceful collages again

By strengthening an edge-decomposition technique for gracefully labelling a generalised Petersen graph, we provide graceful labellings for a new infinite family of such graphs. The method seems flexible enough to provide graceful labellings for many other classes of graphs in the future.

Graceful labellings for an infinite class of generalised Petersen graphs

We exhibit a graceful labelling for each generalised Petersen graph P8t,3 with t ≥ 1. As an easy consequence, we obtain that for any fixed t the corresponding graph is the unique starter graph for a cyclic edgedecomposition of the complete graph K2t+1. Due to its extreme versatility, the technique employed looks promising for finding new graceful labellings, not necessarily involving generalise...