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Distance graphs

2008
*
Proceedings of the fifth international workshop on Foundations of mobile computing - DIAL M-POMC '08
*

To explain the similarities in the connectivity thresholds, we introduce an extension of the random geometric

doi:10.1145/1400863.1400878
dblp:conf/dialm/Avin08
fatcat:3euha2os6rhfddetzgvnsayfpq
*graphs*: the random*distance**graph*, D(n, g): A*graph*resulting from placing n points uniformly ... A random geometric*graph*G(n, r) is a*graph*resulting from placing n points uniformly at random on the unit area disk, and connecting two points iff their Euclidean*distance*is at most the radius r(n). ... that is based on*distance**graphs*. ...##
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Distanced graphs

1992
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Discrete Mathematics
*

These are

doi:10.1016/0012-365x(92)90122-v
fatcat:7a33pxiwzzbdxnt5yiw7f7wupq
*graphs*with additional relation symbols for finite*distances*. Every embedding of*distanced**graphs*is an isometric embedding. ... .,*Distanced**graphs*, Discrete Mathematics 102 (1992) 287-305. This paper studies model theoretic conditions that arise in the study of*distanced**graphs*. ... For*distanced**graphs*, we verify the Amalgamation Property (iii) in Section 3. Condition (v), specialized to the case of*distanced**graphs*, requires that every*distanced**graph*be*distance*finite. ...##
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Distances between directed graphs

1987
*
Časopis pro pěstování matematiky
*

Instead of speaking about the

doi:10.21136/cpm.1987.108565
fatcat:ekbw6yux3jduzdmqgq4kntsjvm
*distance*between isomorphism classes of*graphs*we shall sometimes speak about the*distance*between*graphs*. ... The*distance*between the*graphs*G l9 G 2 is the*distance*between isomorphism classes © l9 © 2 such that G x e © 1? G 2 e © 2 . Now we define the degree vectors of a digraph. ... Let © A , © 2 be two isomorphism classes of directed*graphs*with the same number n of vertices and the same number m of edges. Then 4(®i. ©2) -S m -1 . References ...##
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Steiner distance in graphs

1989
*
Časopis pro pěstování matematiky
*

INTRODUCTION One of the most basic concepts associated with a

doi:10.21136/cpm.1989.118395
fatcat:wrgsavnkqjcp3p3tyfg3rkixbe
*graph*is*distance*. ... THE SIZE OF (n; p)*GRAPHS*Given a nonempty subset S of the vertex set of a connected*graph*G, the*distance*d(S) is the minimum size of a connected*graph*whose vertex set contains S. ...##
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Signed distance graphs

1969
*
Journal of Combinatorial Theory
*

Signed

doi:10.1016/s0021-9800(69)80048-7
fatcat:6dhrt55eqzgqxdi2l4boxymdvq
*graphs*are assigned to systems of points in a metric space. Special cases are investigated. ... It is easy to see that this definition is in conformity with the definition of the*distance**graphs*for the case of a spherical (r-1)-space and the*distance*d = 89 and dasses which can easily be derived ... by a positive edge if and only if the*distance*p(p~, p~) < d, and by a negative edge if and only if p(Pi, Pk) ~ d (hence they are not joined if and only if p(Pi , P~) = d). ...##
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Distance Preserving Graphs
[article]

2015
*
arXiv
*
pre-print

We say a

arXiv:1507.03615v1
fatcat:5cppf5yhsrcilatnikvcbiocwe
*graph*G is*distance*preserving (dp) if it has an isometric subgraph of every possible order up to the order of G. ... We consider how to add a vertex to a dp*graph*so that the result is a dp*graph*. This condition implies that chordal*graphs*are dp. ... The definition of a*distance*-preserving*graph*is similar to the one for*distance*-hereditary*graphs*, but is less restrictive. ...##
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Integral distance graphs

1997
*
Journal of Graph Theory
*

The

doi:10.1002/(sici)1097-0118(199708)25:4<287::aid-jgt6>3.3.co;2-f
fatcat:7ls4d6ehhvdvbkq7k34qsaol4y
*distance**graph*G(Z, D) with*distance*set D is the*graph*with vertex set Z, and two vertices x and y are adjacent if and only if |x − y| ∈ D. ... For each subset D of dist(S), the*distance**graph*G(S, D) with*distance*set D is the*graph*with vertex set S and edge set {{x, y}: d(x, y) ∈ D}. ... Motivated by the*graph*coloring problem, Eggleton [8] considered the following general problem. We refer [1] for general notation and terminology in*graphs*. ...##
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Distance in Graphs
[chapter]

2010
*
Structural Analysis of Complex Networks
*

The

doi:10.1007/978-0-8176-4789-6_3
fatcat:b4xawt5qhzakbizso6yfhyfpxi
*distance*between two vertices is the basis of the definition of several*graph*parameters including diameter, radius, average*distance*and metric dimension. ... We also discuss characterizations of*graph*classes described in terms of*distance*or shortest paths. Finally, generalizations are considered. ... Acknowledgments We would like to thank Peter Dankelmann for sharing his thoughts on average*distance*with us. ...##
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Distance-residual graphs
[article]

2006
*
arXiv
*
pre-print

If we are given a connected finite

arXiv:math/0609810v1
fatcat:pfw44kf6lrbqve3qt2y6v472my
*graph*G and a subset of its vertices V_0, we define a*distance*-residual*graph*as a*graph*induced on the set of vertices that have the maximal*distance*from V_0. ... The relations between the*distance*-residual*graphs*of product*graphs*and their factors are shown. ... Since every*graph*can be a*distance*-residual*graph*, it is a challenge to find wellknown*graphs*as*distance*residuals of some other well-known*graphs*. ...##
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Distance-regular graphs
[article]

2016
*
arXiv
*
pre-print

This is a survey of

arXiv:1410.6294v2
fatcat:s6kq2ydbtzaldcwjk4qgawfawu
*distance*-regular*graphs*. ... We present an introduction to*distance*-regular*graphs*for the reader who is unfamiliar with the subject, and then give an overview of some developments in the area of*distance*-regular*graphs*since the ... A*graph*is called*distance*degree regular if each*distance*-i*graph*is regular. ...##
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?-Unit Distance Graphs

2004
*
Discrete & Computational Geometry
*

We consider a variation on the problem of determining the chromatic number of the Euclidean plane and define the ε-unit

doi:10.1007/s00454-004-1092-8
fatcat:btq7zywx6vfcrfebqh3viogzee
*distance**graph*to be the*graph*whose vertices are the points of E 2 , in which two ... points are adjacent whenever their*distance*is within ε of 1. ... 4 . 4 An ε-unit*distance**graph*with chromatic number 5. ...##
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Distance-Transitive Graphs
[chapter]

1989
*
Distance-Regular Graphs
*

*Distance*-Regular

*Graphs*Definition 2.4.1 We can always find a

*distance*partition for any

*graph*(e.g. example 2.2.2). ... Antipodal

*Graphs*Antipodal

*graphs*are a class of imprimitive

*distance*-transitive

*graphs*. ... They showed that there is only one cubic

*graph*that is

*distance*-regular but not

*distance*-transitive, this being Tutte's (3, 12) -cage (see [37] ). ...

##
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Distance-hereditary graphs

1986
*
Journal of combinatorial theory. Series B (Print)
*

*Distance*-hereditary

*graphs*(sensu Howorka) are connected

*graphs*in which all induced paths are isometric. Examples of such

*graphs*are provided by complete multipartite

*graphs*and ptolemaic

*graphs*. ... Moreover,

*distance*-hereditary

*graphs*are characterized in terms of the

*distance*function d, or via forbidden isometric subgraphs. t-1 ... That is, the

*distance*of any two vertices in an induced path equals their

*distance*in the

*graph*. ...

##
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Distance-Balanced Graphs

2008
*
Annals of Combinatorics
*

*Distance*-balanced

*graphs*are introduced as

*graphs*in which every edge uv has the following property: the number of vertices closer to u than to v is equal to the number of vertices closer to v than to ...

*Distance*-balanced Cartesian and lexicographic products of

*graphs*are also characterized. Several open problems are posed along the way. ...

*Distance*-balanced product

*graphs*In this section we study the conditions under which the standard

*graph*products produce a

*distance*-balanced

*graph*. ...

##
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Integral distance graphs

1997
*
Journal of Graph Theory
*

The

doi:10.1002/(sici)1097-0118(199708)25:4<287::aid-jgt6>3.0.co;2-g
fatcat:4di7q6suzreidbzhotkqacs4sa
*distance**graph*G(Z, D) with*distance*set D is the*graph*with vertex set Z, and two vertices x and y are adjacent if and only if |x − y| ∈ D. ... For each subset D of dist(S), the*distance**graph*G(S, D) with*distance*set D is the*graph*with vertex set S and edge set {{x, y}: d(x, y) ∈ D}. ... Motivated by the*graph*coloring problem, Eggleton [8] considered the following general problem. We refer [1] for general notation and terminology in*graphs*. ...
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