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Homomorphisms of graphs and their global maps
[chapter]

1981
*
Lecture Notes in Computer Science
*

*and*onto

*global*

*maps*

*of*

*homomorphisms*

*of*

*graphs*. ... We can characterize

*homomorphisms*between strongly connected

*graphs*with one-to-one

*and*onto

*global*

*maps*in terms

*of*definiteness

*of*

*their*induced regular

*and*b-regular

*homomorphisms*. Theorem 8. ...

##
###
Cantor–Bernstein type theorem for locally constrained graph homomorphisms

2006
*
European journal of combinatorics (Print)
*

We show that the simultaneous existence

doi:10.1016/j.ejc.2006.06.003
fatcat:sducpzmqd5c5fdraxnur6zu2tq
*of*a single locally surjective*graph**homomorphism*between a*graph*G*and*a connected*and*finite*graph*H together with some locally injective*homomorphism*between ... the same pair*of**graphs*assures that both*homomorphisms*are locally bijective. ... For*graphs*G*and*H a (*graph*)*homomorphism*is a vertex*mapping*f : V G → V H satisfying the property that ( f (u), f (v)) is an edge*of*H whenever vertices u*and*v are adjacent in G. ...##
###
Homomorphisms of Multisource Trees into Networks with Applications to Metabolic Pathways

2007
*
2007 IEEE 7th International Symposium on BioInformatics and BioEngineering
*

We have performed pairwise

doi:10.1109/bibe.2007.4375587
dblp:conf/bibe/ChengHZ07
fatcat:zn667eflfbdo3pch2dqa2wzr4u
*mapping**of*all pathways for four organisms (E. coli, S. cerevisiae, B. subtilis*and*T. thermophilus species)*and*found a reasonably large set*of*statistically significant pathway ... Network*mapping*is a convenient tool for comparing*and*exploring biological networks; it can be used for predicting unknown pathways, fast*and*meaningful searching*of*databases,*and*potentially establishing ... Acknowledgments We thank Professor Pinter*and*Oleg Rokhlenko for giving access to*their*software package MetaPathwayHunter, Professor Karp*and*Dr. ...##
###
Modeling Pointer Redirection as Cyclic Term-graph Rewriting

2007
*
Electronical Notes in Theoretical Computer Science
*

We define first the category

doi:10.1016/j.entcs.2006.10.027
fatcat:jdx7tbgrubfolpbnuetw7kfwqe
*of**graphs*we consider*and*then we define rewrite rules as pairs*of**graph**homomorphisms**of*the form L ← K → R. ... We tackle the problem*of*data-structure rewriting including*global**and*local pointer redirections. ... As in the rest*of*the paper, this*map*is simply denoted ϕ,*and*this is not ambiguous: indeed, if two*graph**homomorphisms*ϕ, ψ : G → H are such that*their*underlying*maps*are equal ϕ = ψ : N G → N H , then ...##
###
Constant-to-one and onto global maps of homomorphisms between strongly connected graphs

1983
*
Ergodic Theory and Dynamical Systems
*

*global*

*map*is finite-to-one

*and*onto,

*and*using them we study the structure

*of*constant-toone

*and*onto

*global*

*maps*

*of*homorphisms between strongly connected

*graphs*

*and*that

*of*constant-to-one

*and*onto ... The

*global*

*maps*

*of*

*homomorphisms*

*of*directed

*graphs*are very closely related to

*homomorphisms*

*of*a class

*of*symbolic dynamical systems called subshifts

*of*finite type. ... )

*and*hence the

*global*

*map*

*of*a

*homomorphism*

*of*

*graphs*is a

*homomorphism*

*of*subshifts

*of*finite type. ...

##
###
Knowledge Representation Analysis of Graph Mining
[article]

2016
*
arXiv
*
pre-print

In short, this problem asks us to find a

arXiv:1608.08956v1
fatcat:qhocefipvzhojfy7mhs2wmem6y
*graph*that frequently occurs as a subgraph among a set*of*example*graphs*. ... In this paper we study the*graph*mining problem as an example*of*a higher order problem. ... Thus, we are required to promote the*homomorphic**mapping*functions to a*global*property in the vocabulary, even though we are only interested in the existence*of*a*mapping*,*and*not in the concrete instance ...##
###
Graph and semigroup homomorphisms on networks of relations

1983
*
Social Networks
*

While the local structure

doi:10.1016/0378-8733(83)90025-4
fatcat:6xf6esikorglpbqscgjf7ztmfq
*of*social roles is captured in a bundle*homomorphism*by putting together points with the same patterns*of*incoming*and*outgoing arrows, the*global*or relational structure*of**their*... To capture the*global*role structure*of*multiplex social relationships, we require a stronger*homomorphism*, one which has properties*of*both the bundle*homomorphism**and*the regular*homomorphism*. ... Let G = (P, R) be a*graph**and*f: P + P' be an onto*map*for some set P'. If R' is the relation on P' induced by R*and*f,*and*G' = (P', R'), then the*map*f: G + G' is a full*graph**homomorphism*. ...##
###
A remark about actions of lattices on free groups

2001
*
Topology and its Applications
*

Every

doi:10.1016/s0166-8641(99)00174-1
fatcat:cdukhizu3rfljp2fiavbd3uahm
*homomorphism*from an irreducible, noncocompact lattice in a higher-rank semisimple Lie group to the outer automorphism group*of*a free group must have a finite image. ... In fact all*homomorphisms*Γ → Out(F n ) arise from actions*of*Γ on finite*graphs*. Corollary 2. Let Γ be as above*and*let ψ : Γ → Out(F n ) be a*homomorphism*. ... Then there is a finite*graph*G with fundamental group F n*and*an action*of*Γ on G by automorphisms such that the induced*homomorphism*Γ → Out(F n ) is ψ. ...##
###
Vicinity Respecting Homomorphisms for Abstracting System Requirements
[chapter]

2010
*
Lecture Notes in Computer Science
*

Vicinity respecting

doi:10.1007/978-3-642-18222-8_1
fatcat:b4bjasmhzrd73cd5xcxk4i5dcy
*homomorphisms*are presented as a means to refine*and*abstract these nets. ... ., dependencies between computational elements*and*they preserve important structural properties*of*nets, such as S-*and*T-components, siphons*and*traps*and*the free choice property. ... They are special*graph**homomorphisms*that are able to formalize abstractions including contractions*of**graphs*not only in*their*breadth but also in*their*length. ...##
###
Local to global property in free groups
[article]

2019
*
arXiv
*
pre-print

The local to

arXiv:1907.05968v2
fatcat:lwbrqsgfdjdzxjdfku3xjhnm6m
*global*property for an equation ψ over a group G asks to show that ψ is solvable in G if*and*only if it is solvable in every finite quotient*of*G. ... In this paper we focus that in order to prove this local to*global*property for free groups G=F_k, it is enough to prove for k less or equal the number*of*parameters in ψ. ... Consider the*map*Γ S → Γ N . The image*of*this*map*is a sub Stallings*graph**of*Γ N corresponding to some Γ H for some H ≤ N . ...##
###
Subgraph Frequencies: Mapping the Empirical and Extremal Geography of Large Graph Collections
[article]

2013
*
arXiv
*
pre-print

In this work, we draw on the theory

arXiv:1304.1548v2
fatcat:entafhr45nhkvp7dtup6gjh2iy
*of**graph**homomorphisms*to formulate*and*analyze such a representation, based on computing the frequencies*of*small induced subgraphs within each*graph*. ... Together, these two complementary frameworks shed light on a fundamental question pertaining to social*graphs*: what properties*of*social*graphs*are 'social' properties*and*what properties are '*graph*' properties ... This work was supported in part by NSF grants IIS-0910664*and*IIS-1016099. ...##
###
Subgraph frequencies

2013
*
Proceedings of the 22nd international conference on World Wide Web - WWW '13
*

In this work, we draw on the theory

doi:10.1145/2488388.2488502
dblp:conf/www/UganderBK13
fatcat:rjtmmwlqdbac7e23vh2xv3g6hm
*of**graph**homomorphisms*to formulate*and*analyze such a representation, based on computing the frequencies*of*small induced subgraphs within each*graph*. ... Together, these two complementary frameworks shed light on a fundamental question pertaining to social*graphs*: what properties*of*social*graphs*are 'social' properties*and*what properties are '*graph*' properties ... This work was supported in part by NSF grants IIS-0910664*and*IIS-1016099. ...##
###
Locally constrained graph homomorphisms—structure, complexity, and applications

2008
*
Computer Science Review
*

A

doi:10.1016/j.cosrev.2008.06.001
fatcat:p57dezmpfjhzpf5xahy4f7rtga
*graph**homomorphism*is an edge preserving vertex*mapping*between two*graphs*. ... Locally constrained*homomorphisms*are those that behave well on the neighborhoods*of*vertices -if the neighborhood*of*any vertex*of*the source*graph*is*mapped*bijectively (injectively, surjectively) to ...*Graph**homomorphisms*are*mappings*between sets*of*vertices*of*two*graphs*having the following property: If two vertices form an edge*of*the source*graph*then*their*images form an edge in the target*graph*...##
###
Graph theory and algorithms

1982
*
Discrete Mathematics
*

N .S~tfho~ou~~~ : The complexity

doi:10.1016/0012-365x(82)90093-0
fatcat:xuedghfhonhylm7uqbmgleu3qi
*of*path problems in*graphs**and*path systems*of*bounded bandwidth. M.-J. Kreowski: A compqrisort between petri-nets*and**graph*gammars. W. ... Reisig: A*graph*grammar rt presentation*of*nonsequential processes. J. Perl/J. Ebert: Reachability*Homomorphisms*on nets. B. Mahr: A bird's_eye view to path problems. P. ... Nasu:*Homomorphisms**of*heir*global**maps*. T. ashiwabara: Algorithms for some intersection*graphs*. T. Asano, &u&i rann N. ...##
###
Page 3788 of Mathematical Reviews Vol. , Issue 84i
[page]

1984
*
Mathematical Reviews
*

Author’s summary: “L

*homomorphisms*, i.e., structure-preserving*mappings*between OL systems, are introduced. ... between synchronous*and*asynchronous cellular spaces, from the point*of*view*of*the equivalence*of**their*respective array transformations with reference to a certain alphabet. ...
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