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graph-homomorphism
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On a non-equilibrium statistical mechanics of graph homomorphisms
, Article Advanced Studies in Theoretical Physics ; Volume 6, Issue 17-20 , 2012 , Pages 815-821 ; 1313311 (ISSN) ; Sharif University of Technology
HIKARI
2012
Abstract
Inspired by the paper [1] we develop a non-equilibrium statistical mechanics for graph homomorphisms, which can be considered as a generalization of several other Markov processes including Ising and parallel Hopfield models. We then apply the theory for the special case of homo-morphisms between rings with N nodes and derive the associated classical Lagrangian in the large N limit
Density and power graphs in graph homomorphism problem
, Article Discrete Mathematics ; Volume 308, Issue 17, 6 September 2008, Pages 4027–4030 ; Hajiabolhassan, Hossein ; Sharif University of Technology
Abstract
We introduce two necessary conditions for the existence of graph homomorphisms based on the concepts of density and power graph. As corollaries, we obtain a lower bound for the fractional chromatic number, and we set forward elementary proofs of the facts that the circular chromatic number of the Petersen graph is equal to three and the fact that the Coxeter graph is a core
Graph homomorphisms and nodal domains [electronic resource]
, Article Linear Algebra and its Applications ; 2006, Volume 418, Issue 1, Pages 44–52 ; Sharif University of Technology
Abstract
In this paper, we derive some necessary spectral conditions for the existence of graph homomorphisms in which we also consider some parameters related to the corresponding eigenspaces such as nodal domains. In this approach, we consider the combinatorial Laplacian and co-Laplacian as well as the adjacency matrix. Also, we present some applications in graph decompositions where we prove a general version of Fisher’s inequality for G-designs
Graph homomorphisms through random walks [electronic resource]
, Article Journal of Graph Theory ; 2003, Volume 44, Issue 1, pages 15–38 ; Hajiabolhassan, Hossein ; Sharif University of Technology
Abstract
In this paper we introduce some general necessary conditions for the existence of graph homomorphisms, which hold in both directed and undirected cases. Our method is a combination of Diaconis and Saloff–Coste comparison technique for Markov chains and a generalization of Haemers interlacing theorem. As some applications, we obtain a necessary condition for the spanning subgraph problem, which also provides a generalization of a theorem of Mohar (1992) as a necessary condition for Hamiltonicity. In particular, in the case that the range is a Cayley graph or an edge-transitive graph, we obtain theorems with a corollary about the existence of homomorphisms to cycles. This, specially, provides...
Graph homomorphisms through random walks
, Article Journal of Graph Theory ; Volume 44, Issue 1 , 2003 , Pages 15-38 ; 03649024 (ISSN) ; Hajiabolhassan, H ; Sharif University of Technology
Wiley-Liss Inc
2003
Abstract
In this paper we introduce some general necessary conditions for the existence of graph homomorphisms, which hold in both directed and undirected cases. Our method is a combination of Diaconis and Saloff-Coste comparison technique for Markov chains and a generalization of Haemers interlacing theorem. As some applications, we obtain a necessary condition for the spanning subgraph problem, which also provides a generalization of a theorem of Mohar (1992) as a necessary condition for Hamiltonicity. In particular, in the case that the range is a Cayley graph or an edge-transitive graph, we obtain theorems with a corollary about the existence of homomorphisms to cycles. This, specially, provides...
On the Graph Pentagon Problem
, M.Sc. Thesis Sharif University of Technology ; Daneshgar, Amir (Supervisor)
Abstract
Density (alias general connectivity) and sparseness are two fundamental notions in mathematics as well as in graph theory. In this thesis we concentrate on Ne{s}et{r}il's Pentagon problem that asks whether there exists a threshold g{0} such that any cubic graph of girth larger than g{0} is homomorphic to the five cycle. We try to explain why this problem is interesting as a question asking the effect of interplay between two contradictory sparseness and density parameters. To be more explicit, we have dedicated the first two chapters to explain and analysis such situations in general and, in particular, in graph theory by providing and explaining similar statements as deep graph-theoretic...
Density and power graphs in graph homomorphism problem
, Article Discrete Mathematics ; Volume 308, Issue 17 , 6 September , 2008 , Pages 4027-4030 ; 0012365X (ISSN) ; Hajiabolhassan, H ; Sharif University of Technology
2008
Abstract
We introduce two necessary conditions for the existence of graph homomorphisms based on the concepts of density and power graph. As corollaries, we obtain a lower bound for the fractional chromatic number, and we set forward elementary proofs of the facts that the circular chromatic number of the Petersen graph is equal to three and the fact that the Coxeter graph is a core. © 2007 Elsevier B.V. All rights reserved
Graph homomorphisms and nodal domains
, Article Linear Algebra and Its Applications ; Volume 418, Issue 1 , 2006 , Pages 44-52 ; 00243795 (ISSN) ; Hajiabolhassan, H ; Sharif University of Technology
2006
Abstract
In this paper, we derive some necessary spectral conditions for the existence of graph homomorphisms in which we also consider some parameters related to the corresponding eigenspaces such as nodal domains. In this approach, we consider the combinatorial Laplacian and co-Laplacian as well as the adjacency matrix. Also, we present some applications in graph decompositions where we prove a general version of Fisher's inequality for G-designs. © 2006 Elsevier Inc. All rights reserved
Natural and Quantum Walks on Graphs
, M.Sc. Thesis Sharif University of Technology ; Daneshgar, Amir (Supervisor)
Abstract
A Markov chain on a base graph is a stochatic process that can be visualized as a particle movement such that the probability of moving from a vertex i to a vertex j is specified by the corresponding transition kernel Ka. In this thesis, based on the result of A.Daneahgar and H.Hajiabolhassa, we recall some general necessary conditions for the existence of graph homomorphism, which holds on both directed and undirected cases. A discrete-time quantum walk on a graph is the repeated application of a unitary evolution operator. In this regard, also, we explain the quantum search algorithm on the result of Grover and the algorithms that is based on the quantum walk approach of A.Ambainis,...
On cylindrical graph construction and its applications
, Article Electronic Journal of Combinatorics ; Volume 23, Issue 1 , 2016 ; 10778926 (ISSN) ; Hejrati, M ; Madani, M ; Sharif University of Technology
Australian National University
2016
Abstract
In this article we introduce the cylindrical construction, as an edge-replacement procedure admitting twists on both ends of the hyperedges, generalizing the concepts of lifts and Pultr templates at the same time. We prove a tensor-hom duality for this construction and we show that not only a large number of well-known graph constructions are cylindrical but also the construction and its dual give rise to some new graph constructions, applications and results. To show the applicability of the main duality we introduce generalized Grötzsch, generalized Petersen-like and Coxeter-like graphs and we prove some coloring properties of these graphs
On Cylindrical Graph Construction and its Applications
, Ph.D. Dissertation Sharif University of Technology ; Daneshgar, Amir (Supervisor)
Abstract
In this thesis we introduce the cylindrical construction, and show that a large number of well-known graph constructions are cylindrical. Then, we prove a tensor-hom duality for this construction and its dual as factors. These fanctors, introduce a reduction from graphs to labeled ones, which is usefull to prove (non-)existance of homomorphisms. By using such reductions,we solve some homomorphism problems from generalized Grotzsch, generalized Petersen-like and Coxeter-like graphs to cycles. Then, we introduce tree cylinders and using them we introduce constructions with smaller maximum degree that do not reduce the girth and odd girth, but preserves homomorphism properties of the given...
Linear index coding via graph homomorphism
, Article Proceedings - 2014 International Conference on Control, Decision and Information Technologies, CoDIT 2014 ; 2014 , pp. 158-163 ; ISBN: 9781479967735 ; Siavoshani, M. J ; Sharif University of Technology
Abstract
In [1], [2] it is shown that the minimum broadcast rate of a linear index code over a finite field Fq is equal to an algebraic invariant of the underlying digraph, called minrankq. In [3], it is proved that for F2 and any positive integer k, minrankq(G) ≤ k if and only if there exists a homomorphism from the complement of the graph G to the complement of a particular undirected graph family called 'graph family {Gk}'. As observed in [2], by combining these two results one can relate the linear index coding problem of undirected graphs to the graph homomorphism problem. In [4], a direct connection between linear index coding problem and graph homomorphism problem is introduced. In contrast to...