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On strong distances in oriented graphs

2003
*
Discrete Mathematics
*

For asymmetric digraphs (that is,

doi:10.1016/s0012-365x(02)00807-5
fatcat:m3qozmkhl5dq3e4xbbszvqoyv4
*oriented**graphs*) we present bounds*on*the*strong*radius*in*terms of order and*on*the*strong*diameter*in*terms of order, girth and connectivity. ... The*strong**distance*between two vertices u and v*in*D, denoted by sdD(u; v) is the minimum size of a strongly connected subdigraph of D containing u and v. ... Bounds*on**strong*diameter*In*this section we present bounds*on*the*strong*diameter of a*strong**oriented**graph*D. ...##
###
Page 7614 of Mathematical Reviews Vol. , Issue 2000k
[page]

2000
*
Mathematical Reviews
*

*strong*

*distance*

*in*

*strong*

*oriented*

*graphs*. ... It is shown that every

*oriented*

*graph*is the

*strong*center of some

*strong*

*oriented*

*graph*. A

*strong*

*oriented*

*graph*D is called strongly self-centered if D is its own

*strong*center. ...

##
###
Lower and upper orientable strong diameters of graphs satisfying the Ore condition

2009
*
Applied Mathematics Letters
*

*In*this work, we determine a bound of the lower

*orientable*

*strong*diameters and the bounds of the upper

*orientable*

*strong*diameters for

*graphs*G = (V , E) satisfying the Ore condition (that is, σ 2 (G) ... Lower and upper

*orientable*

*strong*diameter Lower and upper

*orientable*

*strong*radius

*Strong*

*distance*

*Strong*eccentricity

*Strong*radius and

*strong*diameter The Ore condition a b s t r a c t Let D be a

*strong*... Let D be a

*strong*

*oriented*

*graph*and κ(D) = κ. Then sdiam(D)

*In*[3], Dankelmann et al. also gave an upper bound

*on*the

*strong*radius of a

*strong*

*oriented*

*graph*D. Theorem 6 ([3]). ...

##
###
On $k$-strong distance in strong digraphs

2002
*
Mathematica Bohemica
*

It was shown

doi:10.21136/mb.2002.133957
fatcat:p37kbvmzhbdu5lsilovoxotf2e
*in*[2] that*strong**distance*is a metric*on*the vertex set of a*strong**oriented**graph*D. As such, certain properties are satisfied. ...*In*the*strong**oriented**graph*D of Figure 1 , sd(v, w) = 3, sd(u, y) = 4, and sd(u, x) = 5. A generalization of*distance**in**graphs*was introduced*in*[5] . ...##
###
Page 5313 of Mathematical Reviews Vol. , Issue 2000h
[page]

2000
*
Mathematical Reviews
*

*In*addition, some new char- acterizations as meshed

*graphs*and

*one*

*in*terms of location theory are presented. ... It is shown that every pair r, d of integers with 3 <r <d <2r is realizable as the

*strong*radius and

*strong*diameter of some

*strong*

*oriented*

*graph*. ...

##
###
Minimum average distance of strong orientations of graphs

2004
*
Discrete Applied Mathematics
*

If G is a 2-edge-connected

doi:10.1016/s0166-218x(04)00133-7
fatcat:chteamutnram5lwaavucqiu3dq
*graph*, then˜ min (G) is the minimum average*distance*taken over all*strong**orientations*of G. ... The average*distance*of a*graph*(*strong*digraph) G, denoted by (G) is the average, among the*distances*between all pairs (ordered pairs) of vertices of G. ... For a 2-edge-connected*graph*G,˜ min (G) is the minimum of the average*distances*of*strong**orientations*of G taken over all*strong**orientations*of G. ...##
###
Minimum average distance of strong orientations of graphs

2004
*
Discrete Applied Mathematics
*

If G is a 2-edge-connected

doi:10.1016/j.dam.2004.01.005
fatcat:tbhv4fceybbd7bxe6y6qexquum
*graph*, then˜ min (G) is the minimum average*distance*taken over all*strong**orientations*of G. ... The average*distance*of a*graph*(*strong*digraph) G, denoted by (G) is the average, among the*distances*between all pairs (ordered pairs) of vertices of G. ... For a 2-edge-connected*graph*G,˜ min (G) is the minimum of the average*distances*of*strong**orientations*of G taken over all*strong**orientations*of G. ...##
###
The optimal strong radius and optimal strong diameter of the Cartesian product graphs

2011
*
Applied Mathematics Letters
*

[Justie Su-Tzu Juan, Chun-Ming Huang, I-Fan Sun, The

doi:10.1016/j.aml.2010.12.001
fatcat:n6hmbgh23ffmfejqzmyc5yzbuy
*strong**distance*problem*on*the Cartesian product of*graphs*, Inform. Process. ... The optimal*strong*radius (resp.*strong*diameter) srad(G) (resp. sdiam(G)) of a*graph*G is the minimum*strong*radius (resp.*strong*diameter) over all*strong**orientations*of G. ... Some known results*on*the*strong**distance*,*strong*radius and*strong*diameter can be found*in*[3] [4] [5] . ...##
###
Page 5745 of Mathematical Reviews Vol. , Issue 2003h
[page]

2003
*
Mathematical Reviews
*

*In*this paper it is shown that, for each integer k > 2, every

*oriented*

*graph*is the k-

*strong*center of some

*strong*digraph. ... Martin Knor (SK-STU; Bratislava) 2003h:05075 05Ci2 05C20 Zhang, Ping |Zhang, Ping®] (1-WMI-DM; Kalamazoo, MI)

*On*k-

*strong*

*distance*

*in*

*strong*digraphs. (English summary) Math. ...

##
###
Page 4745 of Mathematical Reviews Vol. , Issue 92i
[page]

1992
*
Mathematical Reviews
*

It is proven

*in*this paper that for any two*oriented**graphs*D, and D, and positive integer k, there exists a*strong**oriented**graph*H whose m-center and m-median are isomorphic to D, and D>, respectively ... i(C) is an*orientation*-preserving curve*on*S. ...##
###
Note on the relation between radius and diameter of a graph

1995
*
Mathematica Bohemica
*

Paper [3] notes that if we have any

doi:10.21136/mb.1995.126222
fatcat:h4dupvc3kbanbdjiwp7zrotu3u
*distance**on**graphs*which is a metric and then define eccentricity, radius, and diameter as usual*in*terms of this metric, then the corresponding inequality holds. ...*In*this note we prove that for any natural numbers r ^ 1, d > 2r there exists a*strong*digraph D with radius r and diameter d. (*Distance*and eccentricity are the usual*ones*.) ...##
###
Strong embeddings of minimum genus

2010
*
Discrete Mathematics
*

Waterloo, 1977), pp. 341-355, Academic Press, 1979]) asserts that every bridgeless cubic

doi:10.1016/j.disc.2010.03.019
fatcat:6gctsgfi65etrkn4lms2s6r53e
*graph*can be embedded*on*a surface of its own genus*in*such a way that the face boundaries are cycles of the*graph*... to the order of these*graphs*), thus providing plethora of*strong*counterexamples to the above conjecture. ... This is no longuer true*on*the torus. Figure 1 shows two embeddings of a non-planar cubic*graph**in*the torus.*One*is*strong*, and the other*one*is not. ...##
###
Shattering, Graph Orientations, and Connectivity
[article]

2012
*
arXiv
*
pre-print

These examples are derived from properties of

arXiv:1211.1319v1
fatcat:paxrxebd6rbivccft24xw2f2be
*orientations*related to*distances*and flows*in*networks. ...*In**one*direction, we use this connection to derive results*in**graph*theory. Our main tool is a generalization of the Sauer-Shelah Lemma. ... The work developed from results*in*the Master thesis of Shay Moran; we would like to acknowledge again the contribution of the advisor of this thesis -Ami Litman. ...##
###
Oriented graphs with prescribed $m$-center and $m$-median

1991
*
Czechoslovak Mathematical Journal
*

*Oriented*

*graphs*with prescribed m-center and m-median ... The maximum

*distance*or m-

*distance*md{u, v) between u and v is max {d(u,v), d(v, u)}. It is not difficult to show that the m-

*distance*is a metric

*on*the vertex set of a

*strong*digraph. ... For vertices u and v

*in*a

*strong*digraph D, the directed

*distance*d(u, v) is the length ofa shortest (directed) u -v path

*in*D. ...

##
###
Page 5774 of Mathematical Reviews Vol. , Issue 95j
[page]

1995
*
Mathematical Reviews
*

(SA-NTL; Durban)

*On*the integrity of*distance*domination*in**graphs*. (English summary) Australas. J. Combin. 10 (1994), 29-43. ...*In*this paper, we show that the*strong*embedding conjecture for chain*graphs*is equivalent to the*strong*embed- ding conjecture. ...
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