We present several constructions for terraces for cyclic groups that are zigzag terraces, graceful terraces or both. These allow us to complete the classification of imperfect twizzler terraces, unify several previously unrelated constructions of terraces from the literature, find terraces for some non-cyclic abelian groups, and show that for any given r the Oberwolfach Problem with parameters ...

In this paper we study a technique to transform α-labeled trees into ρ-labeled forests. We use this result to prove that the complete graph K2n+1 can be decomposed into these types of forests. In addition we show a robust family of trees that admit ρ-labelings, we use this result to describe the set of all trees for which a ρ-labeling must be found to completely solve Kotzig’s conjecture about ...

In this paper we establish that the Lovász θ function on a graph can be restated as a kernel learning problem. We introduce the notion of SVM−θ graphs, on which Lovász θ function can be approximated well by a Support vector machine (SVM). We show that Erdös-Rényi random G(n, p) graphs are SVM−θ graphs for log4 n n ≤ p< 1. Even if we embed a large clique of size Θ (√ np 1−p ) in a G(n, p) graph ...

A graceful n-permutation is a graceful labeling of an n-vertex path Pn. In this paper we improve the asymptotic lower bound on the number of such permutations from Ω((5/3)n) to Ω(2.37n). This is a computer-assisted proof based on an effective algorithm that enumerates graceful n-permutations. Our algorithm is also presented in detail. 1. Graceful graphs and permutations Let G = (V,E) be an undi...

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

Graceful labelling is studied on undirected graphs since graceful graphs can be used in some H-decomposition problems. In this note, we investigate the directed graceful problem for many orientations of undirected trees with short diameters, and provide some directed trees that deny any digraceful labelling. AMS Subject Classification (2000): 05C78

A Smarandache-Fibonacci triple is a sequence S(n), n ≥ 0 such that S(n) = S(n − 1) + S(n − 2), where S(n) is the Smarandache function for integers n ≥ 0. Clearly, it is a generalization of Fibonacci sequence and Lucas sequence. Let G be a (p, q)-graph and {S(n)|n ≥ 0} a Smarandache-Fibonacci triple. An bijection f : V (G) → {S(0), S(1), S(2), . . . , S(q)} is said to be a super Smarandache-Fibo...

In this work some new odd graceful graphs are investigated. We prove that the graph obtained by fusing all the n vertices of Cn of even order with the apex vertices of n copies of K1,m admits odd graceful labeling. In addition to this we show that the shadow graphs of path Pn and star K1,n are odd graceful graphs.