2019
DOI: 10.1016/j.laa.2019.03.012
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Bounds for the matching number and cyclomatic number of a signed graph in terms of rank

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Cited by 22 publications
(11 citation statements)
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“…Lemma 2.7. [7] Let (G, σ) be a signed graph. If (H, σ) is an induced subgraph of (G, σ), then r(G, σ) ≥ r(H, σ).…”
Section: Preliminariesmentioning
confidence: 99%
See 1 more Smart Citation
“…Lemma 2.7. [7] Let (G, σ) be a signed graph. If (H, σ) is an induced subgraph of (G, σ), then r(G, σ) ≥ r(H, σ).…”
Section: Preliminariesmentioning
confidence: 99%
“…Belardo et al investigated the spectral characterizations and the Laplacian coefficients of signed graphs in [1] and [2], respectively. He et al studied the relation between the rank of a signed graph and the matching number of its underlying graph in [7]. Li et al [10] studied the rank of a signed graph in terms of independence number.…”
Section: Introductionmentioning
confidence: 99%
“…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%
“…Guo et al [6] and Liu et al [12] introduced the Hermitian adjacency matrix of a mixed graph and presented some basic properties of the rank of the mixed graphs independently. In [4], the rank of the signed unicyclic graph was discussed by Fan et al He et al characterized the relation among the rank, the matching number and the cyclomatic number of a signed graph in [7]. Chen et al [3] investigated the relation between the H-rank of a mixed graph and the matching number of its underlying graph.…”
Section: Introductionmentioning
confidence: 99%