On certain classes of graceful lobsters

On edge graceful labelings of disjoint unions of 2r-regular edge graceful graphs

We prove that if G is a 2r-regular edge graceful (p, q) graph with (r, kp) = 1 then kG is edge graceful for odd k. We also prove that for certain specific classes of 2r-regular edge graceful graphs it is possible to drop the requirement that (r, kp) = 1

Constraint Programming Models for Graceful Graphs

The problem of finding a graceful labelling of a graph, or proving that the graph is not graceful, has previously been modelled as a CSP. A new and much faster CSP model of the problem is presented, with several new results for graphs whose gracefulness was previously unknown. Several classes of graph that are conjectured to be graceful only for small instances are investigated: after a certain...

α Valuations of Special Classes of Quadratic Graphs

-graceful labelings of partial cubes

7 Partial cubes are graphs that allow isometric embeddings into hypercubes. -graceful labelings of partial cubes are introduced as a natural extension of graceful labelings of trees. It is shown that several classes of partial cubes are -graceful, for instance even 9 cycles, Fibonacci cubes, and (newly introduced) lexicographic subcubes. The Cartesian product of -graceful partial cubes is again...

Decompositions of complete multipartite graphs via generalized graceful labelings

We prove the existence of infinite classes of cyclic Γ-decompositions of the complete multipartite graph, Γ being a caterpillar, a hairy cycle or a cycle. All results are obtained by the construction of d-divisible α-labelings of Γ, introduced in [A. Pasotti, On d-graceful labelings, Ars Combin. 111 (2013), 207–223] as a generalization of classical α-labelings. It is known that such labelings i...