The first step in graph-based semi-supervised classification is to construct a graph from input data. While the k-nearest neighbor graphs have been the de facto standard method of graph construction, this paper advocates using the less well-known mutual k-nearest neighbor graphs for high-dimensional natural language data. To compare the performance of these two graph construction methods, we ru...

It has recently been observed by Zuiddam that finite graphs form a preordered commutative semiring under the graph homomorphism preorder together with join and disjunctive product as addition multiplication, respectively. This led to new characterization of Shannon capacity $\Theta$ via Strassen's Positivstellensatz: $\Theta(\bar{G}) = \inf_f f(G)$, where $f : \mathsf{Graph} \to \mathbb{R}_+$ r...

We establish the existence of vertex-magic total labelings (VMTLs) for several infinite classes of regular graphs. The main method of construction is to assemble a number of appropriately labeled copies of one graph into a single graph with a VMTL. This method enables us for example to begin with any even-regular graph and from it construct a cubic graph possessing a VMTL. An important feature ...

Motivated by copying models of the web graph, Bonato and Janssen [3] introduced the following simple construction: given a graph G, for each vertex x and each subset X of its closed neighbourhood, add a new vertex y whose neighbours are exactly X. Iterating this construction yields a limit graph ↑G. Bonato and Janssen claimed that the limit graph is independent of G, and it is known as the infi...

The D-eigenvalues {µ1,…,µp} of a graph G are the eigenvalues of its distance matrix D and form its D-spectrum. The D-energy, ED(G) of G is given by ED (G) =∑i=1p |µi|. Two non cospectral graphs with respect to D are said to be D-equi energetic if they have the same D-energy. In this paper we show that if G is an r-regular graph on p vertices with 2r ≤ p - 1, then the complements of iterated lin...

Graph-based Semi-Supervised Learning (SSL) methods have had empirical success in a variety of domains, ranging from natural language processing to bioinformatics. Such methods consist of two phases. In the first phase, a graph is constructed from the available data; in the second phase labels are inferred for unlabeled nodes in the constructed graph. While many algorithms have been developed fo...

We describe a graph-based global registration method for creating 2D mosaic images. When multi-frames overlap in space, global registration is necessary to minimize the accumulated registration errors. We use a graph to represent the temporal and spatial connectivity and show that global registration can be obtained through the search for an optimal path in the constructed graph. The definition...

We describe a sufficient condition for graphs used in a construction of Thomassen (which yields hypohamiltonian graphs) to produce maximally non-hamiltonian (MNH) graphs as well. Then we show that the Coxeter graph fulfils this sufficient condition, and thus applying the Thomassen’s construction to multiple copies of the Coxeter graph yields infinitely many MNH graphs with girth 7. So far, the ...