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WEAK UNCERTAINTY PRINCIPLE FOR FRACTALS,GRAPHS AND METRIC MEASURE SPACES
Uncertainty principle p.c.f. fractal Heisenberg’s inequality measure metric spaces Poincar′ e inequality self-similar graphs Sierpinski ′ gasket uniform finitely ramified graphs
2015/12/10
We develop a new approach to formulate and prove the weak uncertainty inequality which was recently introduced by Okoudjou and Strichartz.We assume either an appropriate measure growth condition with ...
Chip-Firing and Rotor-Routing on Directed Graphs
Chip-Firing Rotor-Routing Directed Graphs
2015/8/14
We give a rigorous and self-contained survey of the abelian sandpile model and rotor-router model on finite directed graphs, highlighting the connections between them. We present several intriguing op...
Graphs of Hecke operators
Graphs Hecke operators
2011/2/21
Let X be a curve over F q with function field F. In this paper, we define a graph for each Hecke operator with fixed ramification. A priori, these graphs can be seen as a convenient
language to organ...
Tuza conjectured that for every graph G, the maximum size of a set of edge-disjoint triangles and minimum size of a set of edges meeting all triangles, satisfy 2.
Image denoising by regularization on characteristic graphs
Image Restoration Denoising, Graph Regularization
2010/9/27
This paper introduces improvements to a now classical family of image denoising methods through rather minimal changes to the way derivatives are computed. In particular, we ask, and answer, the quest...
We conjecture that every oriented graph $G$ on $n$ vertices with $\delta ^+ (G) , \delta ^- (G) \geq 5n/12$ contains the square of a Hamilton cycle. We also give a conjectural bound on the minimum sem...
We determine all graphs whose matching polynomials have at most five distinct zeros. As a consequence, we find new families of graphs which are determined by their matching polynomial. In particular, ...
On the metric dimension of corona product graphs
Resolving sets metric dimension corona graph
2010/12/6
Given a set of vertices S = {v1, v2, ..., vk} of a connected graph G, the metric representation of a vertex v of G with respect to S is the vector r(v|S) = (d(v, v1), d(v, v2), ..., d(v, vk )), where ...
Vertex, edge and total coloring in spider graphs
Vertex coloring Edge- coloring Total coloring
2010/9/13
In this paper we investigate the vertex chromatic number, the edge chromatic number, and the total chromatic number in Spider graphs.
Let G = (V,E) be a graph with p vertices an q edges. A graph G is said to admit a triangular sum labeling if its vertices can be labeled by non-negative integers such that induced edge labels obtained...
In this paper the new coloring of planar, VEF-coloring, will be introduced. A VEF coloring of a simple planar graph G is a proper coloring of all elements, including vertices, edges and faces of G. We...
Energy and some Hamiltonian properties of graphs
Energy of graphs Hamiltonian property of graphs
2010/9/17
Using the energy of graphs, we present sufficient conditions for some Hamiltonian properties of graphs.
The energy of a graph is defined as the sum of the absolute values of its eigenvalues. In this paper, we obtain an upper bound for the energy of a graph that involves its moments.
A remark on total domination critical graphs
Total domination total domination critical graph
2010/9/14
A graph G with no isolated vertex is total domination vertex critical if for any vertex v of G that is not adjacent to a vertex of degree one, the total domination number of G−v is less than the...
The Lattice of Threshold Graphs
Automorphism group Distributive lattice Eigenvalue Graphic partition Laplacian spectrum Order ideal Poset
2008/6/26
Due in part to their many interesting properties, a family of graphs has been studied under a variety of names, by various authors, since the late 1970's. Only recently has it become apparent that the...