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Signed degree sequences of signed graphs

1997
*
Journal of Graph Theory
*

This paper gives necessary and sufficient conditions for an integral

doi:10.1002/(sici)1097-0118(199710)26:2<111::aid-jgt6>3.0.co;2-v
fatcat:lhsnco5bczhorbfsxoedbogsku
*sequence*to be the*signed**degree**sequence**of*a*signed**graph*or a*signed*tree, answering a question raised by Chartrand et al. ... An integral*sequence*is s-graphical if it is the*signed**degree**sequence**of*a*signed**graph*. ... . , d p is the*signed**degree**sequence**of*a*signed**graph*G, then −σ : −d 1 , −d 2 , . . . , −d p is the*signed**degree**sequence**of*the*signed**graph*G obtained from G by interchanging positive edges with ...##
###
Signed degree sequences in signed multipartite graphs

2015
*
Hacettepe Journal of Mathematics and Statistics
*

In this paper, we characterize

doi:10.15672/hjms.2015449661
fatcat:xelsgh7vubhkxoeoae2lyp4fwq
*signed**degree**sequences**of**signed*k-partite*graphs*. Also, we give the existence*of**signed*k-partite*graphs*with given*signed**degree*sets. ... The set*of*distinct*signed**degrees**of*the vertices in a*signed*k-partite*graph*G(V1, V2, · · · , V k ) is called its*signed**degree*set. ... An integral*sequence*is s-graphical if it is the*signed**degree**sequence**of*a*signed**graph*. ...##
###
The convex hull of degree sequences of signed graphs

2009
*
Discrete Mathematics
*

Jordon,

doi:10.1016/j.disc.2008.05.043
fatcat:7gw4jfcibjeqjl5bi5g7ud6mui
*Signed**graph*factors and*degree**sequences*, J.*Graph*Theory 52 (2006) 27-36], the*degree**sequences**of**signed**graphs*can be characterized by a system*of*linear inequalities. ... In this paper, we show that P n is the convex hull*of*the set*of**degree**sequences**of**signed**graphs**of*order n. We also determine many properties*of*P n , including a characterization*of*its vertices. ...*Signed**degree**sequences**of**signed**graphs*were studied in [6] and it was shown that a*sequence**of*real numbers is the*degree**sequence**of*a*signed**graph*if and only if the*sequence*satisfies the system ...##
###
Signed degree sets in signed bipartite graphs
[article]

2006
*
arXiv
*
pre-print

In this paper, we prove that every set

arXiv:math/0609122v2
fatcat:xr4sb5fe25f2xlt3pbl33cjnxm
*of*integers is the*signed**degree*set*of*some connected*signed*bipartite*graph*. \medskip \medskip ... The set S*of*distinct*signed**degrees**of*the vertices*of*G(U, V) is called its*signed**degree*set. ... An integral*sequence*is s-graphical if it is the*signed**degree**sequence**of*a*signed**graph*. ...##
###
Signed degree sets in signed graphs

2007
*
Czechoslovak Mathematical Journal
*

The set

doi:10.1007/s10587-007-0079-z
fatcat:hd3gjdteyrh45bfimfwl274nnq
*of*distinct*signed**degrees**of*the vertices*of*a*signed*3-partite*graph*is called its*signed**degree*set. ... In this paper, we prove that every set*of*n integers is the*signed**degree*set*of*some connected*signed*3-partite*graph*. ... An integral*sequence*is s-graphical if it is the*signed**degree**sequence**of*a*signed**graph*. ...##
###
On signed degrees in signed graphs

1994
*
Czechoslovak Mathematical Journal
*

The

doi:10.21136/cmj.1994.128488
fatcat:eellu4tdbreyndtatxxmx2hfum
*degree**sequence**of*a*signed**graph*S has the*signed**degrees*in nonincreasing order. The*degree**sequence**of*the*signed**graph*S*of*Figure 1 is, therefore, 2, 2, 0, -1, -1. ... Then it is clear that S is a*signed**graph*with*degree**sequence*a. Conversely, let a be the*degree**sequence**of*a*signed**graph*. Then there exists a*signed**graph*T having*degree**sequence*a. ...##
###
Signed degree sets in signed graphs
[article]

2006
*
arXiv
*
pre-print

The set D

arXiv:math/0609121v1
fatcat:2kv2nl4bdjf7vjuus7tnv42eyq
*of*distinct*signed**degrees**of*the vertices in a*signed**graph*G is called its*signed**degree*set. ... We also prove that every non-empty set*of*integers is the*signed**degree*set*of*some connected*signed**graph*. ... A*sequence*σ = [d 1 , d 2 , ..., d n integers is graphical if σ is a*signed**degree**sequence**of*some*signed**graph*. ...##
###
A note on signed degree sets in signed bipartite graphs

2008
*
Applicable Analysis and Discrete Mathematics
*

The authors are grateful to the referee for valuable comments and suggestions which improved the presentation

doi:10.2298/aadm0801114p
fatcat:txfzzv6ntbfp5p7buztqe3gaju
*of*the paper. ... The various characterizations*of**signed**degree**sequences*in*signed**graphs*can be found in [1, 7] , and one such criterion [1] is similar to Hakimi's result for*degree**sequences*in*graphs*[2] . ... A*signed**degree**sequence*σ = [d 1 , d 2 , . . . , d n ]*of*a*signed**graph*G is formed by listing the vertex*signed**degrees*in non-increasing order. ...##
###
Page 5982 of Mathematical Reviews Vol. , Issue 2004h
[page]

2004
*
Mathematical Reviews
*

A finite

*sequence**of*nonnegative integers is said to be a graphical*sequence*if it is the*degree**sequence**of*some*graph*. ... The*signed*2-independence number*of*a*graph*G, denoted a2(G), is the maximum weight*of*a*signed*2-independence function*of*G. In this article, we give some new upper bounds on a? ...##
###
Knot graphs

2000
*
Journal of Graph Theory
*

Any

doi:10.1002/(sici)1097-0118(200005)34:1<100::aid-jgt9>3.0.co;2-r
fatcat:7hmzvhbgizgebj37fsreob5xhq
*graph*which is reducible by some finite*sequence**of*these moves, to a*graph*with no edges is called a knot*graph*. ... We show that the class*of*knot*graphs*strictly contains the set*of*delta-wye*graphs*. ... D Delete any pair*of*parallel edges e, f with opposite*signs*; contract any pair*of*edges e, f with opposite*signs*and e, f incident with a common vertex*of**degree*2. ...##
###
Knot graphs

2000
*
Journal of Graph Theory
*

Any

doi:10.1002/(sici)1097-0118(200005)34:1<100::aid-jgt9>3.3.co;2-i
fatcat:lridt4ouvjaerdly7dnnaqh2ku
*graph*which is reducible by some finite*sequence**of*these moves, to a*graph*with no edges is called a knot*graph*. ... We show that the class*of*knot*graphs*strictly contains the set*of*delta-wye*graphs*. ... D Delete any pair*of*parallel edges e, f with opposite*signs*; contract any pair*of*edges e, f with opposite*signs*and e, f incident with a common vertex*of**degree*2. ...##
###
Frustration in signed graphs
[article]

2014
*
arXiv
*
pre-print

Also, we obtain a bound for these invariants in a special class

arXiv:1403.7212v1
fatcat:unux5pscwfdorpwswbcht2hcfq
*of**signed**graphs*. ... Zaslavsky conjectured the following: The minimum number*of*vertices to be deleted to restore balance in a subcubic*signed**graph*is the same as the minimum number*of*edges to be deleted to restore balance ... Acknowledgements The work presented here is part*of*my Ph.D. dissertation [3] written under the guidance*of*Neil Robertson at The Ohio State University. ...##
###
Toward a Laplacian spectral determination of signed ∞-graphs

2018
*
Filomat
*

*of*the

*signed*∞-

*graphs*containing a triangle. ... Matrices can be associated to

*signed*

*graphs*and the question whether a

*signed*

*graph*is determined by the set

*of*its eigenvalues has gathered the attention

*of*several researchers. ... Acknowledgments The authors are grateful to the unknown referee for his/her fruitful remarks which led to an improved presentation

*of*our results. ...

##
###
On signed diagonal flip sequences

2011
*
European journal of combinatorics (Print)
*

It states that any triangulation

doi:10.1016/j.ejc.2010.12.001
fatcat:xynj3n7u3ncgdghobe5im4ukwe
*of*a polygon can be transformed into another triangulation*of*the same polygon by a*sequence**of**signed*diagonal flips. ... In this paper we give a sufficient and necessary condition for a diagonal flip*sequence*to be a*signed*diagonal flip*sequence*. ... ((i) ⇒ (ii)) If a*sequence**of*diagonal flips ϕ is a*sequence**of**signed*diagonal flips then this induces a 2-coloring on the*graph*G(ϕ) by coloring each vertex ϕ(i) with the*sign**of*the triangles on its ...##
###
Page 5483 of Mathematical Reviews Vol. , Issue 98I
[page]

1998
*
Mathematical Reviews
*

(RC-NCT-AM; Hsinchu)

*Signed**degree**sequences**of**signed**graphs*. (English summary) J.*Graph*Theory 26 (1997), no.2, 111-117. ... This paper gives necessary and sufficient condi- tions for an integral*sequence*to be the*signed**degree**sequence**of*a*signed**graph*or a*signed*tree. ...
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