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...

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...

Graph labeling is considered as one of the most interesting areas in graph theory. A for a simple G (numbering or valuation), an association non -negative integers to vertices G&amp;nbsp; (vertex labeling) edges (edge both them. In this paper we study graceful k- uniform hypertree and define condition corresponding tree be graceful. if minimum difference vertices&amp;rsquo; labels each edge dis...

Graceful labelings use a prominent place among difference vertex labelings. In this work we present new families of graceful graphs all of them obtained applying a general substitution result. This substitution is applied here to replace some paths with some trees with a more complex structures. Two caterpillars with the same size are said to be textit{analogous} if thelarger stable sets, in bo...

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...