10,084 research outputs found
On the spectral characterizations of 3-rose graphs
A rose graph with p petals (or p-rose graph) is a graph obtained by taking p cycles with just a vertex in common. In this paper, we prove that all 3-rose graphs, having at least one triangle, are determined by their Laplacian spectra and all 3-rose graphs axe determined by their signless Laplacian spectra
On the spectral radii and the signless Laplacian spectral radii of c-cyclic graphs with fixed maximum degree
AbstractIf G is a connected undirected simple graph on n vertices and n+c-1 edges, then G is called a c-cyclic graph. Specially, G is called a tricyclic graph if c=3. Let Δ(G) be the maximum degree of G. In this paper, we determine the structural characterizations of the c-cyclic graphs, which have the maximum spectral radii (resp. signless Laplacian spectral radii) in the class of c-cyclic graphs on n vertices with fixed maximum degree Δ⩾n+c+12. Moreover, we prove that the spectral radius of a tricyclic graph G strictly increases with its maximum degree when Δ(G)⩾1+6+2n32, and identify the first six largest spectral radii and the corresponding graphs in the class of tricyclic graphs on n vertices
Dual concepts of almost distance-regularity and the spectral excess theorem
Generally speaking, ‘almost distance-regular’ graphs are graphs that share some, but not necessarily all, regularity properties that characterize distance-regular graphs. In this paper we first
propose two dual concepts of almost distance-regularity. In some cases, they coincide with concepts introduced before by other authors, such as partially distance-regular graphs. Our study focuses on finding out when almost distance-regularity leads to distance-regularity. In particular, some ‘economic’ (in the sense of minimizing the number of conditions) old and new
characterizations of distance-regularity are discussed. Moreover, other characterizations based on the average intersection numbers and the recurrence coefficients are obtained. In some cases, our results can also be seen as a generalization of the
so-called spectral excess theorem for distance-regular graphs.Peer Reviewe
Product Multicommodity Flow in Wireless Networks
We provide a tight approximate characterization of the -dimensional
product multicommodity flow (PMF) region for a wireless network of nodes.
Separate characterizations in terms of the spectral properties of appropriate
network graphs are obtained in both an information theoretic sense and for a
combinatorial interference model (e.g., Protocol model). These provide an inner
approximation to the dimensional capacity region. These results answer
the following questions which arise naturally from previous work: (a) What is
the significance of in the scaling laws for the Protocol
interference model obtained by Gupta and Kumar (2000)? (b) Can we obtain a
tight approximation to the "maximum supportable flow" for node distributions
more general than the geometric random distribution, traffic models other than
randomly chosen source-destination pairs, and under very general assumptions on
the channel fading model?
We first establish that the random source-destination model is essentially a
one-dimensional approximation to the capacity region, and a special case of
product multi-commodity flow. Building on previous results, for a combinatorial
interference model given by a network and a conflict graph, we relate the
product multicommodity flow to the spectral properties of the underlying graphs
resulting in computational upper and lower bounds. For the more interesting
random fading model with additive white Gaussian noise (AWGN), we show that the
scaling laws for PMF can again be tightly characterized by the spectral
properties of appropriately defined graphs. As an implication, we obtain
computationally efficient upper and lower bounds on the PMF for any wireless
network with a guaranteed approximation factor.Comment: Revised version of "Capacity-Delay Scaling in Arbitrary Wireless
Networks" submitted to the IEEE Transactions on Information Theory. Part of
this work appeared in the Allerton Conference on Communication, Control, and
Computing, Monticello, IL, 2005, and the Internation Symposium on Information
Theory (ISIT), 200
Some spectral and quasi-spectral characterizations of distance-regular graphs
© . This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/In this paper we consider the concept of preintersection numbers of a graph. These numbers are determined by the spectrum of the adjacency matrix of the graph, and generalize the intersection numbers of a distance-regular graph. By using the preintersection numbers we give some new spectral and quasi-spectral characterizations of distance-regularity, in particular for graphs with large girth or large odd-girth. (C) 2016 Published by Elsevier Inc.Peer ReviewedPostprint (author's final draft
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