Let M G be the centered Hardy-Littlewood maximal operator on a finite graph . We find lim p → ∞ ‖ when is start ( S n ) and complete K ), we fully describe corresponding extremizers for ∈ 1 , 2 prove that = + ≥ 25 Also, compute best constant C such every f : V R have Var ≤ − / all 3 characterize extremizers. Moreover, Z

We consider problems that can be characterized by large dynamic graphs. Communication networks provide the prototypical example of such problems where nodes in the graph are network IDs and the edges represent communication between pairs of network IDs. In such graphs, nodes and edges appear and disappear through time so that methods that apply to static graphs are not suucient. We introduce a ...

Recently, sparse and low-rank graph-based discriminant analysis (SLGDA) has yielded satisfactory results in hyperspectral image (HSI) dimensionality reduction (DR), for which sparsity and low-rankness are simultaneously imposed to capture both local and global structure of hyperspectral data. However, SLGDA fails to exploit the spatial information. To address this problem, a tensor sparse and l...

We first consider some problems related to the maximum number of dominating (or strong dominating) sets in a regular graph. Our techniques, centered around Shearer’s entropy lemma, extend to a reasonably broad class of graph parameters enumerating vertex colorings that satisfy conditions on the multiset of colors appearing in neighborhoods (either open or closed). Dominating sets and strong dom...

We introduce a generalization of the Yao graph where the cones used are adaptively centered on a set of nearest neighbors for each node, thus creating a directed or undirected spanning subgraph of a given unit disk graph (UDG). We also permit the apex of the cones to be positioned anywhere along the line segment between the node and its nearest neighbor, leading to a class of Yao-type subgraphs...

The definition of efficient similarity or dissimilarity measures between graphs is a key problem in structural pattern recognition. This problem is nicely addressed by the graph edit distance, which constitutes one of the most flexible graph dissimilarity measure in this field. Unfortunately, the computation of an exact graph edit distance is known to be exponential in the number of nodes. In t...

The face-centered cubic grid is a three dimensional 12-regular infinite grid. This graph represents an optimal way to pack spheres in the three-dimensional space. In this grid, vertices represent and edges contact between spheres. We give lower upper bounds on chromatic number of d th power particular, case = 2 we prove that 13. also determine sharper for 3 subgraphs