A classic result is that the number of distinct eigenvalues of a graph of diameter d is at least d+1. More generally, let G be a graph with n vertices, and let S(G) denote the set of all symmetric n by n matrices, A = [aij ], with the property that for off-diagonal entries, aij is nonzero if and only if G has an edge from i to j. The traditional proof of the classic result extends to A ∈ S(G). ...

A fundamental problem in wireless networks is the minimum spanning tree (MST) problem: given a set V of wireless nodes, compute a spanning tree T , so that the total cost of T is minimized. In recent years, there has been a lot of interest in the physical interference model based on SINR constraints. Distributed algorithms are especially challenging in the SINR model, because of the non-localit...

It is known from algebraic graph theory that if L the Laplacian matrix of some tree G with a vertex degree sequence d=(δ1,…,δn)⊤ and D its distance matrix, then LD+2I=(2⋅1−d)1⊤, where 1 an all-ones column vector. We prove converse proposition: this identity holds for d D, essentially tree, matrix. This result immediately generalizes to weighted graphs. Therefore, above bilinear equation in L, c...

An out-tree T of a directed graph D is a rooted tree subgraph with all arcs directed outwards from the root. An out-branching is a spanning out-tree. By l(D) and ls(D) we denote the maximum number of leaves over all out-trees and out-branchings of D, respectively. We give fixed parameter tractable algorithms for deciding whether ls(D) ≥ k and whether l(D) ≥ k for a digraph D on n vertices, both...

Orchard intensification is motivated by the desire to produce fruit early in the life of the orchard to rapidly recover establishment costs. Intensification is possible using dwarfing rootstocks that control tree size, induce early cropping and produce large quantities of fruit compared to the amount of wood produced. Therefore, this study attempts to compare some yield and fruit properties of ...

background: dermatophagoides farinae and dermatophagoides pteronyssinus are house dust mites (hdm) that they cause severe asthma and allergic symptoms. tropomyosin protein plays an important role in mentioned immune and allergic reactions to hdms. here, tropomyosin protein from dermatophagoides spp. was comprehensively screened in silico for its allergenicity, antigenicity and similarity/conser...

Chaudhari S. R. ,Komejwar D. D. , On Fuzzy Pushdown Automata and their covering , International Journal of Computer Applications Vol. 46(8),2012 pp 27-33 Comon H. ,Dauchet M. ,Gilleron R. ,Jacquemard F. , Lugiez D. ,Loding C. ,Tison S. , and Tommasi M. , Tree Automata: techniques and apllications. (2007) Lee E. T. Fuzzy tree automata and syntactic pattern recognition, IEEE Trans Pattern Anal Ma...

In this paper we show how to find nearly optimal embeddings of large trees in several natural classes of graphs. The size of the tree T can be as large as a constant fraction of the size of the graph G, and the maximum degree of T can be close to the minimum degree of G. For example, we prove that any graph of minimum degree d without 4-cycles contains every tree of size ǫd and maximum degree a...

As the size of phylogenetic databases grows, the need for efficiently searching these databases arises. Thanks to previous and ongoing research, searching by attribute value and by text has become commonplace in these databases. However, searching by topological or physical structure, especially for large databases and especially for approximate matches, is still an art. We propose structural s...