Signed degree sets in signed graphs

Pirzada, S.; Naikoo, T. A.; Dar, Farooq Ahmad

doi:10.1007/s10587-007-0079-z

Cited by 6 publications

(12 citation statements)

References 6 publications

(6 reference statements)

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“…such that there exist a a isigned graph G with global signed score set Theorem 22 (Pirzada, Naikoo, Dar [47]) Let p be a positive integer and γ = {g 1 , g 2 , . .…”

Section: Theoremmentioning

confidence: 99%

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Tripartite graphs with given degree set

Iványi

Pirzada

Dar

2015

Acta Universitatis Sapientiae, Informatica

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If k ≥ 1, then the global degree set of a k-partite graph G = (V1, V2, . . . , Vk, E) is the set of the distinct degrees of the vertices of G, while if k ≥ 2, then the distributed degree set of G is the family of the k degree sets of the vertices of the parts of G. We propose algorithms to construct bipartite and tripartite graphs with prescribed global and distributed degree sets consisting from arbitrary nonnegative integers. We also present a review of the similar known results on digraphs.

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“…such that there exist a a isigned graph G with global signed score set Theorem 22 (Pirzada, Naikoo, Dar [47]) Let p be a positive integer and γ = {g 1 , g 2 , . .…”

Section: Theoremmentioning

confidence: 99%

“…Proof. See [47] In 2013 Kumar, Sarma, and Sawlami [29] studied the number of vertices and multiplicity of degrees as parameters of directed and undirected tree realizations of prescribed degree sets.…”

Section: Theoremmentioning

confidence: 99%

Tripartite graphs with given degree set

Iványi

Pirzada

Dar

2015

Acta Universitatis Sapientiae, Informatica

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“…For the definitions and the eigenvalues of the following graph products available for (unsigned) graph, one may refer to [5] and the same for signed graphs can be found in [8].…”

Section: Preliminariesmentioning

confidence: 99%

“…In the examples given in the main section, we use the following lemmas found in [7] and [8]. We follow the notation, [r], for an integer r, such that [r] = 0 if r is even and [r] = 1 if it is odd.…”

Section: Preliminariesmentioning

confidence: 99%

On composition of signed graphs

Hameed¹,

Germina²

2012

Discuss. Math. Graph Theory

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A graph whose edges are labeled either as positive or negative is called a signed graph. In this article, we extend the notion of composition of (unsigned) graphs (also called lexicographic product) to signed graphs. We employ Kronecker product of matrices to express the adjacency matrix of this product of two signed graphs and hence find its eigenvalues when the second graph under composition is net-regular. A signed graph is said to be net-regular if every vertex has constant net-degree, namely, the difference of the number of positive and negative edges incident with a vertex. We also characterize balance in signed graph composition and have some results on the Laplacian matrices of this product.

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“…In [4], Kapoor et al proved that every set of positive integers is the degree set of some connected graph and determined the smallest order for such a graph. Pirzada et al [6] proved that every set of positive (negative) integers is the signed degree set of some connected signed graph and determined the smallest possible order for such a signed graph.…”

Section: Introductionmentioning

confidence: 99%

A note on signed degree sets in signed bipartite graphs

Pirzada¹,

Naikoo²,

Dar³

2008

Appl. Anal. Discrete Math.

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A signed bipartite graph G(U, V) is a bipartite graph in which each edge is assigned a positive or a negative sign. The signed degree of a vertex x in G(U, V) is the number of positive edges incident with x less the number of negative edges incident with x. The set S of distinct signed degrees of the vertices of G(U, V) is called its signed degree set. In this paper, we prove that every set of integers is the signed degree set of some connected signed bipartite graph.

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Signed degree sets in signed graphs

Cited by 6 publications

References 6 publications

Tripartite graphs with given degree set

Tripartite graphs with given degree set

On composition of signed graphs

A note on signed degree sets in signed bipartite graphs

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