Ghorbani, Ebrahim; Haemers, Willem H.; Reza Maimani, Hamid; Parsaei Majd, Leila On sign-symmetric signed graphsArs Mathematica Contemporane 2020: 83–93
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).
Akbari, Saieed; Reza Maimani, Hamid; Parsaei Majd, Leila; Wanless, Ian M. Zero-sum flows for Steiner systemsDiscrete Mathematics 2020: 112074
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.
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
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.