2021 [ nach oben ]

Haemers, Willem H; Parsaei Majd, Leila Spectral symmetry in conference matricesDesigns, Codes and Cryptography 2021: 1–8
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A conference matrix of order \(n\) is an \(n \times n\) matrix \(C\) with diagonal entries \(0\) and off-diagonal entries \(\pm 1\) satisfying \(CC^T = (n - 1) I \). If \(C\) is symmetric, then \(C\) has a symmetric spectrum \(\sum\) (that is, \( \sum = - \sum \) ) and eigenvalues \(\pm \sqrt{n-1}\). We show that many principal submatrices of \(C\) also have symmetric spectrum, which leads to examples of Seidel matrices of graphs (or, equivalently, adjacency matrices of complete signed graphs) with a symmetric spectrum. In addition, we show that some Seidel matrices with symmetric spectrum can be characterized by this construction.
@article{haemers2021spectral, abstract = {A conference matrix of order \(n\) is an \(n \times n\) matrix \(C\) with diagonal entries \(0\) and off-diagonal entries \(\pm 1\) satisfying \(CC^T = (n - 1) I \). If \(C\) is symmetric, then \(C\) has a symmetric spectrum \(\sum\) (that is, \( \sum = - \sum \) ) and eigenvalues \(\pm \sqrt{n-1}\). We show that many principal submatrices of \(C\) also have symmetric spectrum, which leads to examples of Seidel matrices of graphs (or, equivalently, adjacency matrices of complete signed graphs) with a symmetric spectrum. In addition, we show that some Seidel matrices with symmetric spectrum can be characterized by this construction.}, author = {Haemers, Willem H and Parsaei Majd, Leila}, journal = {Designs, Codes and Cryptography}, keywords = {sys:relevantfor:ae leilaparsaeimajd willemhhaemers year2021}, pages = {1–8}, title = {Spectral symmetry in conference matrices}, year = 2021 }

2020 [ nach oben ]

Ghorbani, Ebrahim; Haemers, Willem H.; Reza Maimani, Hamid; Parsaei Majd, Leila On sign-symmetric signed graphsArs Mathematica Contemporane 2020: 83–93
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A signed graph is said to be sign-symmetric if it is switching isomorphic to its negation. Bipartite signed graphs are trivially sign-symmetric. We give new constructions of non-bipartite sign-symmetric signed graphs. Sign-symmetric signed graphs have a symmetric spectrum but not the other way around. We present constructions of signed graphs with symmetric spectra which are not sign-symmetric. This, in particular answers a problem posed by Belardo, Cioabua}, Koolen, and Wang (2018).
@article{ghorbani2020signsymmetric, abstract = {A signed graph is said to be sign-symmetric if it is switching isomorphic to its negation. Bipartite signed graphs are trivially sign-symmetric. We give new constructions of non-bipartite sign-symmetric signed graphs. Sign-symmetric signed graphs have a symmetric spectrum but not the other way around. We present constructions of signed graphs with symmetric spectra which are not sign-symmetric. This, in particular answers a problem posed by Belardo, Cioab\u{a}, Koolen, and Wang (2018).}, author = {Ghorbani, Ebrahim and Haemers, Willem H. and Reza Maimani, Hamid and Parsaei Majd, Leila}, journal = {Ars Mathematica Contemporane}, keywords = {sys:relevantfor:ae amc ebrahimghorbani hamidrezamaimani leilaparsaeimajd willemhhaemers year2020}, pages = {83–93}, title = {On sign-symmetric signed graphs}, year = 2020 }

Akbari, Saieed; Reza Maimani, Hamid; Parsaei Majd, Leila; Wanless, Ian M. Zero-sum flows for Steiner systemsDiscrete Mathematics 2020: 112074
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Abstract. Given a \(t-(v, k, \lambda)\) design, \(D = (X, B)\), a zero-sum \(n\)-flow of \(D\) is a map \(f : \mathcal{B longrightarrow pm 1, . . . , pm (n − 1)\}\) such that for any point \(x \in X\), the sum of \(f\) over all blocks incident with \(x\) is zero. For a positive integer \(k\), we find a zero-sum \(k\)-flow for an STS(uw) and for an \(STS(2v + 7)\) for \(v equiv 1 (mod 4)\), if there are \(STS(u)\), \(STS(w)\) and \(STS(v)\) such that the \(STS(u)\) and \(STS(v)\) both have a zero-sum \(k\)-flow. In 2015, it was conjectured that for \(v > 7\) every \(STS(v)\) admits a zero-sum 3-flow. Here, it is shown that many cyclic \(STS(v)\) have a zero-sum 3-flow. Also, we investigate the existence of zero-sum flows for some Steiner quadruple systems.
@article{rezamaimani2020zerosum, abstract = {Abstract. Given a \(t-(v, k, \lambda)\) design, \(D = (X, B)\), a zero-sum \(n\)-flow of \(D\) is a map \(f : \mathcal{B} \longrightarrow \{\pm 1, . . . , \pm (n − 1)\}\) such that for any point \(x \in X\), the sum of \(f\) over all blocks incident with \(x\) is zero. For a positive integer \(k\), we find a zero-sum \(k\)-flow for an STS(uw) and for an \(STS(2v + 7)\) for \(v \equiv 1 (mod 4)\), if there are \(STS(u)\), \(STS(w)\) and \(STS(v)\) such that the \(STS(u)\) and \(STS(v)\) both have a zero-sum \(k\)-flow. In 2015, it was conjectured that for \(v > 7\) every \(STS(v)\) admits a zero-sum 3-flow. Here, it is shown that many cyclic \(STS(v)\) have a zero-sum 3-flow. Also, we investigate the existence of zero-sum flows for some Steiner quadruple systems.}, author = {Akbari, Saieed and Reza Maimani, Hamid and Parsaei Majd, Leila and Wanless, Ian M.}, journal = {Discrete Mathematics}, keywords = {sys:relevantfor:ae dm hamidrezamaimani ianmwanless leilaparsaeimajd saieedakbari year2020}, pages = 112074, title = {Zero-sum flows for Steiner systems}, year = 2020 }

Alizadeh, Faezeh; Maimani, Hamid Reza; Parsaei Majd, Leila; Rajabi Parsa, Mina Roman 2-domination in graphs and graph productsIranian Journal of Mathematical Sciences and Informatics Iranian Journal of Mathematical Sciences and Informatics 2020
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For a graph \(G = (V, E)\) of order n, a Roman 2-dominating function \(f : V \to \0, 1, 2\}\) has the property that for every vertex \(v \in V\) with \(f(v) = 0\), either \(v\) is adjacent to a vertex assigned 2 under \(f\) , or \(v\) is adjacent to at least two vertices assigned 1 under \(f\). In this paper, we classify all graphs with Roman 2-domination number belonging to the set \(\{2, 3, 4, n - 2, n - 1, n\}\). Furthermore, we obtain some results about Roman 2-domination number of some graph operations.
@article{noauthororeditor2020roman, abstract = {For a graph \(G = (V, E)\) of order n, a Roman {2}-dominating function \(f : V \to \{0, 1, 2\}\) has the property that for every vertex \(v \in V\) with \(f(v) = 0\), either \(v\) is adjacent to a vertex assigned 2 under \(f\) , or \(v\) is adjacent to at least two vertices assigned 1 under \(f\). In this paper, we classify all graphs with Roman {2}-domination number belonging to the set \(\{2, 3, 4, n - 2, n - 1, n\}\). Furthermore, we obtain some results about Roman {2}-domination number of some graph operations.}, author = {Alizadeh, Faezeh and Maimani, Hamid Reza and Parsaei Majd, Leila and Rajabi Parsa, Mina}, journal = {Iranian Journal of Mathematical Sciences and Informatics Iranian Journal of Mathematical Sciences and Informatics}, keywords = {sys:relevantfor:ae faezealizadeh hamidrezamaimani leilaparsaeimajd minarajabiparsa year2020}, title = {Roman {2}-domination in graphs and graph products}, year = 2020 }

2019 [ nach oben ]

Reza Maimani, Hamid; Parsaei Majd, Leila Nowhere-zero flow on some products of signed graphsDiscrete Applied Mathematics 2019: 84–92
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Abstract In this paper, we show that the Cartesian product of two signed nontrivial connected graphs has a nowhere-zero 4-flow. Also, we prove that signed biwheel \(B_n\) admits a nowhere zero \(k\)-flow where \(k \in \{3,4\}\).
@article{rezamaimani2019nowherezero, abstract = {Abstract In this paper, we show that the Cartesian product of two signed nontrivial connected graphs has a nowhere-zero 4-flow. Also, we prove that signed biwheel \(B_n\) admits a nowhere zero \(k\)-flow where \(k \in \{3,4\}\).}, author = {Reza Maimani, Hamid and Parsaei Majd, Leila}, journal = {Discrete Applied Mathematics}, keywords = {sys:relevantfor:ae dam hamidrezamaimani leilaparsaeimajd year2019}, pages = {84–92}, title = {Nowhere-zero flow on some products of signed graphs}, year = 2019 }

2018 [ nach oben ]

Akbari, Saieed; Maimani, Hamid Reza; Majd, Leila Parsaei On the spectrum of some signed complete and complete bipartite graphsFilomat 2018: 5817–5826
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In this paper, we obtain the spectrum of signed complete and complete bipartite graphs whose negative edges form a matching. Moreover, we construct a family of signed complete graphs having symmetric spectrum.
@article{akbari2018spectrum, abstract = {In this paper, we obtain the spectrum of signed complete and complete bipartite graphs whose negative edges form a matching. Moreover, we construct a family of signed complete graphs having symmetric spectrum.}, author = {Akbari, Saieed and Maimani, Hamid Reza and Majd, Leila Parsaei}, journal = {Filomat}, keywords = {sys:relevantfor:ae hamidrezamaimani leilaparsaeimajd saieedakbari year2018}, pages = {5817-5826}, title = {On the spectrum of some signed complete and complete bipartite graphs}, year = 2018 }

Akbari, Saieed; Haemers, Willem H; Maimani, Hamid Reza; Majd, Leila Parsaei Signed graphs cospectral with the pathLinear Algebra and its Applications 2018: 104–116
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A signed graph \(\Gamma\) is said to be determined by its spectrum if every signed graph with the same spectrum as \(\Gamma\) is switching isomorphic with \(\Gamma\). Here it is proved that the path \(P_n\), interpreted as a signed graph, is determined by its spectrum if and only if \( n equiv 0, 1, or 2 (\text{mod 4)\), unless \(n \in \8, 13, 14, 17, 29\ \), or \(n = 3\).
@article{akbari2018signed, abstract = {A signed graph \(\Gamma\) is said to be determined by its spectrum if every signed graph with the same spectrum as \(\Gamma\) is switching isomorphic with \(\Gamma\). Here it is proved that the path \(P_n\), interpreted as a signed graph, is determined by its spectrum if and only if \( n \equiv 0, 1, or 2 (\text{mod} 4)\), unless \(n \in \{8, 13, 14, 17, 29\} \), or \(n = 3\).}, author = {Akbari, Saieed and Haemers, Willem H and Maimani, Hamid Reza and Majd, Leila Parsaei}, journal = {Linear Algebra and its Applications}, keywords = {sys:relevantfor:ae hamidrezamaimani leilaparsaeimajd saieedakbari willemhhaemers year2018}, pages = {104–116}, title = {Signed graphs cospectral with the path}, year = 2018 }

2015 [ nach oben ]

Parsaei Majd, Leila; Rahimi, Ahad On the structure of sequentially Cohen-Macaulay bigraded modulesCzechoslovak Mathematical Journal 2015: 1011–1022
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Let \(K\) be a field and \(S = K[x_1, \dots, x_m, y_1, \dots, y_n ]\) be the standard bigraded polynomial ring over \(K\). In this paper, we explicitly describe the structure of finitely generated bigraded ”sequentially Cohen–Macaulay” \(S\)-modules with respect to \(Q = (y_1, \dots, y_n )\). Next, we give a characterization of sequentially Cohen–Macaulay modules with respect to \(Q\) in terms of local cohomology modules. Cohen–Macaulay modules that are sequentially Cohen–Macaulay with respect to \(Q\) are considered.
@article{parsaeimajd2015structure, abstract = {Let \(K\) be a field and \(S = K[x_1, \dots, x_m, y_1, \dots, y_n ]\) be the standard bigraded polynomial ring over \(K\). In this paper, we explicitly describe the structure of finitely generated bigraded ”sequentially Cohen–Macaulay” \(S\)-modules with respect to \(Q = (y_1, \dots, y_n )\). Next, we give a characterization of sequentially Cohen–Macaulay modules with respect to \(Q\) in terms of local cohomology modules. Cohen–Macaulay modules that are sequentially Cohen–Macaulay with respect to \(Q\) are considered.}, author = {Parsaei Majd, Leila and Rahimi, Ahad}, journal = {Czechoslovak Mathematical Journal}, keywords = {sys:relevantfor:ae ahadrahimi leilaparsaeimajd year2015}, pages = {1011-1022}, title = {On the structure of sequentially Cohen-Macaulay bigraded modules}, year = 2015 }