Skew-rank of an oriented graph in terms of matching number

Ma, Xiaobin; Wong, Dein; Tian, Fenglei

doi:10.1016/j.laa.2016.01.036

Cited by 51 publications

(17 citation statements)

References 14 publications

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“…is exactly the number of cycles if the cycles of G are pairwise vertex-disjoint. Then Corollary 1.2 is equivalent to Theorem 1.3 below when G is bipartite, obtained in [16], showing the correlation between the skew-rank of an oriented graph, the matching number, and the dimension of cycle space of its underlying graph.…”

Section: Resultsmentioning

confidence: 83%

Relation between the skew-rank of an oriented graph and the independence number of its underlying graph

Huang

Wang

2018

J Comb Optim

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An oriented graph G σ is a digraph without loops or multiple arcs whose underlying graph is G. Let S (G σ ) be the skew-adjacency matrix of G σ and α(G) be the independence number of G. The rank of S(G σ ) is called the skew-rank of G σ , denoted by sr(G σ ). Wong et al.[European J. Combin. 54 (2016) 76-86] studied the relationship between the skew-rank of an oriented graph and the rank of its underlying graph. In this paper, the correlation involving the skew-rank, the independence number, and some other parameters are considered. First we show that sr(G σ ) + 2α(G)

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Section: Resultsmentioning

confidence: 83%

Relation between the skew-rank of an oriented graph and the independence number of its underlying graph

Huang

Wang

2018

J Comb Optim

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“…After that, there are a lot of related results. The most studied is the rank of oriented graph by using different parameters, such as r(G) [21], m(G) [22], bicyclic oriented graphs [23][24][25], independence number [26], and so on.…”

Section: Introductionmentioning

confidence: 99%

A lower bound of the rank of a signed graph in terms of order and maximum degree

Yong¹,

Xu²

2021

ScienceAsia

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“…Collatz et al [1] had wanted to obtain all graphs of order n with r(G) < n. Until today, this problem is also unsolved. In mathematics, the rank (or nullity, inertia index) of a graph has attracted a lot of researchers' attention, they focus on the bounds for the rank (or nullity, inertia index) of a simple graph G [4,6,11,23,24,25,26,34], a signed graph [3,5,8,15,19,32], an oriented graph [12,14,16,20,21,28] and a mixed graph [2,29] and so on.…”

Section: Introductionmentioning

confidence: 99%

Inertia indices of a complex unit gain graph in terms of matching number

Lu¹,

Wu²

2021

Preprint

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A complex unit gain graph is a triple ϕ = (G, T, ϕ) (or G ϕ for short) consisting of a simple graph G, as the underlying graph of G ϕ , the set of unit complex numbers T = z ∈ C : |z| = 1 and a gain function ϕ :− → E → T such that ϕ(e i,j ) = ϕ(e j,i ) −1 . Let A(G ϕ ) be adjacency matrix of G ϕ . In this paper, we prove thatwhere p(G ϕ ), n(G ϕ ), m(G) and c(G) are the number of positive eigenvalues of A(G ϕ ), the number of negative eigenvalues of A(G ϕ ), the matching number and the cyclomatic number of G, respectively. Furthermore, we characterize the graphs which attain the upper bounds and the lower bounds, respectively.

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Skew-rank of an oriented graph in terms of matching number

Cited by 51 publications

References 14 publications

Relation between the skew-rank of an oriented graph and the independence number of its underlying graph

Relation between the skew-rank of an oriented graph and the independence number of its underlying graph

A lower bound of the rank of a signed graph in terms of order and maximum degree

Inertia indices of a complex unit gain graph in terms of matching number

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