Author

# Hamid Reza Maimani

Other affiliations: University of Tehran

Bio: Hamid Reza Maimani is an academic researcher from Shahid Rajaee Teacher Training University. The author has contributed to research in topics: Bipartite graph & Vertex-transitive graph. The author has an hindex of 15, co-authored 90 publications receiving 1329 citations. Previous affiliations of Hamid Reza Maimani include University of Tehran.

##### Papers published on a yearly basis

##### Papers

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TL;DR: In this paper, it was shown that if G and H are two non-abelian finite groups such that Γ G ≅ Γ H, then | G | = | H |, then H is nilpotent.

304 citations

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TL;DR: In this paper, it was shown that if R is a local commutative ring with at least 33 elements, and Γ ( R )≠∅, then Γ( R ) is not planar.

184 citations

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TL;DR: In this paper, the basic properties of a ring with nonzero identity are investigated and some characterization results regarding connectedness, chromatic index, diameter, girth, and planarity are given.

Abstract: Let R be a ring with nonzero identity. The unit graph of R, denoted by G(R), has its set of vertices equal to the set of all elements of R; distinct vertices x and y are adjacent if and only if x + y is a unit of R. In this article, the basic properties of G(R) are investigated and some characterization results regarding connectedness, chromatic index, diameter, girth, and planarity of G(R) are given. (These terms are defined in Definitions and Remarks 4.1, 5.1, 5.3, 5.9, and 5.13.)

112 citations

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TL;DR: In this paper, the diameter of a subgraph of a commutative ring consisting of non-unit elements was characterized and the connectedness and diameter of the subgraph was characterized.

Abstract: Let $R$ be a commutative ring with identity. Let $\Gamma(R)$ be a graph with vertices as elements of $R$, where two distinct vertices $a$ and $b$ are adjacent if and only if $Ra+Rb=R$. In this paper we consider a subgraph $\Gamma_2(R)$ of $\Gamma(R)$ which consists of non-unit elements. We look at the connectedness and the diameter of this graph. We completely characterize the diameter of the graph $\Gamma_2(R)\setminus\J(R)$. In addition, it is shown that for two finite semi-local rings $R$ and $S$, if $R$ is reduced, then $\Gamma(R)\cong\Gamma(S)$ if and only if $R\cong S$.

102 citations

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TL;DR: In this article, the diameter of a subgraph Γ 2 (R ) of a commutative ring with identity is characterized and the connectedness and diameter of this subgraph is analyzed.

101 citations

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TL;DR: In this article, the expectation and covariance matrix of the Wishart distribution are derived, where the expectation is derived from the expectation matrix of a square matrix containing only zeros and ones.

Abstract: The commutation matrix $K$ is defined as a square matrix containing only zeroes and ones. Its main properties are that it transforms vecA into vecA', and that it reverses the order of a Kronecker product. An analytic expression for $K$ is given and many further properties are derived. Subsequently, these properties are applied to some problems connected with the normal distribution. The expectation is derived of $\varepsilon' A\varepsilon\cdot\varepsilon' B\varepsilon\cdot\varepsilon'C\varepsilon$, where $\varepsilon \sim N(0, V)$, and $A, B, C$ are symmetric. Further, the expectation and covariance matrix of $x \otimes y$ are found, where $x$ and $y$ are normally distributed dependent variables. Finally, the variance matrix of the (noncentral) Wishart distribution is derived.

443 citations

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01 Jan 2009

TL;DR: In this article, the authors introduce the concept of graph operations and modifications, and characterizations of spectra by characterizations by spectra and one eigenvalue, and Laplacians.

Abstract: Preface 1. Introduction 2. Graph operations and modifications 3. Spectrum and structure 4. Characterizations by spectra 5. Structure and one eigenvalue 6. Spectral techniques 7. Laplacians 8. Additional topics 9. Applications Appendix Bibliography Index of symbols Index.

398 citations

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01 Jan 1994

TL;DR: For the list object, introduced in Chapter 5, it was shown that each data element contains at most one predecessor element and one successor element, so for any given data element or node in the list structure, the authors can talk in terms of a next element and a previous element.

Abstract: For the list object, introduced in Chapter 5, it was shown that each data element contains at most one predecessor element and one successor element. Therefore, for any given data element or node in the list structure, we can talk in terms of a next element and a previous element.

381 citations