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Signed degree sequences of signed graphs

Jing-Ho Yan, Ko-Wei Lih, David Kuo, Gerard J. Chang
1997 Journal of Graph Theory  
This paper gives necessary and sufficient conditions for an integral 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  ... 
doi:10.1002/(sici)1097-0118(199710)26:2<111::aid-jgt6>3.0.co;2-v fatcat:lhsnco5bczhorbfsxoedbogsku

Signed degree sequences in signed multipartite graphs

S. Pirzada
2015 Hacettepe Journal of Mathematics and Statistics  
In this paper, we characterize 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.  ... 
doi:10.15672/hjms.2015449661 fatcat:xelsgh7vubhkxoeoae2lyp4fwq

The convex hull of degree sequences of signed graphs

Heather Jordon, Richard McBride, Shailesh Tipnis
2009 Discrete Mathematics  
Jordon, 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  ... 
doi:10.1016/j.disc.2008.05.043 fatcat:7gw4jfcibjeqjl5bi5g7ud6mui

Signed degree sets in signed bipartite graphs [article]

S. Pirzada, T. A. Naikoo, F. A. Dar
2006 arXiv   pre-print
In this paper, we prove that every set 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.  ... 
arXiv:math/0609122v2 fatcat:xr4sb5fe25f2xlt3pbl33cjnxm

Signed degree sets in signed graphs

S. Pirzada, T. A. Naikoo, F. A. Dar
2007 Czechoslovak Mathematical Journal  
The set 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.  ... 
doi:10.1007/s10587-007-0079-z fatcat:hd3gjdteyrh45bfimfwl274nnq

On signed degrees in signed graphs

Gary Chartrand, Heather Gavlas, Frank Harary, Michelle Schultz
1994 Czechoslovak Mathematical Journal  
The 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.  ... 
doi:10.21136/cmj.1994.128488 fatcat:eellu4tdbreyndtatxxmx2hfum

Signed degree sets in signed graphs [article]

S. Pirzada, T. A. Naikoo, F. A. Dar
2006 arXiv   pre-print
The set D 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 .  ... 
arXiv:math/0609121v1 fatcat:2kv2nl4bdjf7vjuus7tnv42eyq

A note on signed degree sets in signed bipartite graphs

S. Pirzada, T.A. Naikoo, F.A. Dar
2008 Applicable Analysis and Discrete Mathematics  
The authors are grateful to the referee for valuable comments and suggestions which improved the presentation 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.  ... 
doi:10.2298/aadm0801114p fatcat:txfzzv6ntbfp5p7buztqe3gaju

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

S. D. Noble, D. J. A. Welsh
2000 Journal of Graph Theory  
Any 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.  ... 
doi:10.1002/(sici)1097-0118(200005)34:1<100::aid-jgt9>3.0.co;2-r fatcat:7hmzvhbgizgebj37fsreob5xhq

Knot graphs

S. D. Noble, D. J. A. Welsh
2000 Journal of Graph Theory  
Any 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.  ... 
doi:10.1002/(sici)1097-0118(200005)34:1<100::aid-jgt9>3.3.co;2-i fatcat:lridt4ouvjaerdly7dnnaqh2ku

Frustration in signed graphs [article]

Vaidy Sivaraman
2014 arXiv   pre-print
Also, we obtain a bound for these invariants in a special class 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.  ... 
arXiv:1403.7212v1 fatcat:unux5pscwfdorpwswbcht2hcfq

Toward a Laplacian spectral determination of signed ∞-graphs

Mohammad Iranmanesh, Mahboubeh Saheli
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.  ... 
doi:10.2298/fil1806283i fatcat:ypq5bcgw2bgflozsumjlqvp4xi

On signed diagonal flip sequences

Rui Pedro Carpentier
2011 European journal of combinatorics (Print)  
It states that any triangulation 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  ... 
doi:10.1016/j.ejc.2010.12.001 fatcat:xynj3n7u3ncgdghobe5im4ukwe

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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