http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
SEMISYMMETRIC CUBIC GRAPHS OF ORDER 34p<sup>3</sup>
Darafsheh, Mohammad Reza,Shahsavaran, Mohsen Korean Mathematical Society 2020 대한수학회보 Vol.57 No.3
A simple graph is called semisymmetric if it is regular and edge transitive but not vertex transitive. Let p be a prime. Folkman proved [J. Folkman, Regular line-symmetric graphs, Journal of Combinatorial Theory 3 (1967), no. 3, 215-232] that no semisymmetric graph of order 2p or 2p<sup>2</sup> exists. In this paper an extension of his result in the case of cubic graphs of order 34p<sup>3</sup>, p ≠ 17, is obtained.
CHARACTERIZATION OF THE GROUPS Dp+1(2) AND Dp+1(3) USING ORDER COMPONENTS
Mohammad Reza Darafsheh 대한수학회 2010 대한수학회지 Vol.47 No.2
In this paper we will prove that the groups Dp+1(2) and Dp+1(3), where p is an odd prime number, are uniquely determined by their sets of order components. A main consequence of our result is the validity of Thompson’s conjecture for the groups Dp+1(2) and Dp+1(3).
On non-isomorphic groups with the same set of order components
Mohammad Reza Darafsheh 대한수학회 2008 대한수학회지 Vol.45 No.1
In this paper we will prove that the simple groups Bp(3) and Cp(3), p an odd prime number, are 2-recognizable by the set of their order components. More precisely we will prove that if G is a finite group and OC(G) denotes the set of order components of G, then OC(G) = OC(Bp(3)) if and only if G = Bp(3) or Cp(3) In this paper we will prove that the simple groups Bp(3) and Cp(3), p an odd prime number, are 2-recognizable by the set of their order components. More precisely we will prove that if G is a finite group and OC(G) denotes the set of order components of G, then OC(G) = OC(Bp(3)) if and only if G = Bp(3) or Cp(3)
A characterization of the group A22 by non-commuting graph
Mohammad Reza Darafsheh,Pedram Yosefzadeh 대한수학회 2013 대한수학회보 Vol.50 No.1
Let G be a finite non-abelian group. We define the noncommuting graph ∇(G) of G as follows: the vertex set of ∇(G) is G−Z(G) and two vertices x and y are adjacent if and only if xy 6≠ yx. In this paper we prove that if G is a finite group with ∇(G) ≅ ∇(A22), then G = A22, where A22 is the alternating group of degree 22.
ON NON-ISOMORPHIC GROUPS WITH THE SAME SET OF ORDER COMPONENTS
Darafsheh, Mohammad Reza Korean Mathematical Society 2008 대한수학회지 Vol.45 No.1
In this paper we will prove that the simple groups $B_p(3)\;and\;G_p(3)$, p an odd prime number, are 2-recognizable by the set of their order components. More precisely we will prove that if G is a finite group and OC(G) denotes the set of order components of G, then OC(G) = $OC(B_p(3))$ if and only if $G{\cong}B_p(3)\;or\;C_p(3)$.
A CHARACTERIZATION OF THE GROUP A<sub>22</sub> BY NON-COMMUTING GRAPH
Darafsheh, Mohammad Reza,Yosefzadeh, Pedram Korean Mathematical Society 2013 대한수학회보 Vol.50 No.1
Let G be a finite non-abelian group. We define the non-commuting graph ${\nabla}(G)$ of G as follows: the vertex set of ${\nabla}(G)$ is G-Z(G) and two vertices x and y are adjacent if and only if $xy{\neq}yx$. In this paper we prove that if G is a finite group with $${\nabla}(G){\simeq_-}{\nabla}(\mathbb{A}_{22})$$, then $$G{\simeq_-}\mathbb{A}_{22}$$where $\mathbb{A}_{22}$ is the alternating group of degree 22.
Semisymmetric cubic graphs of order 34p³
Mohammad Reza Darafsheh,Mohsen Shahsavaran 대한수학회 2020 대한수학회보 Vol.57 No.3
A simple graph is called semisymmetric if it is regular and edge transitive but not vertex transitive. Let $p$ be a prime. Folkman proved [J.~Folkman, {\it Regular line-symmetric graphs}, Journal of Combinatorial Theory {\bf 3} (1967), no. 3, 215--232] that no semisymmetric graph of order $2p$ or $2p^2$ exists. In this paper an extension of his result in the case of cubic graphs of order $34p^3$, $p\neq 17$, is obtained.
CHARACTERIZATION OF THE GROUPS D<sub>p+1</sub>(2) AND D<sub>p+1</sub>(3) USING ORDER COMPONENTS
Darafsheh, Mohammad Reza Korean Mathematical Society 2010 대한수학회지 Vol.47 No.2
In this paper we will prove that the groups $D_{p+1}$(2) and $D_{p+1}$(3), where p is an odd prime number, are uniquely determined by their sets of order components. A main consequence of our result is the validity of Thompson's conjecture for the groups $D_{p+1}$(2) and $D_{p+1}$(3).
Semi-symmetric cubic graph of order $12p^3$
Pooriya Majd Amoli,Mohammad Reza Darafsheh,Abolfazl Tehranian 대한수학회 2022 대한수학회보 Vol.59 No.1
A simple graph is called semi-symmetric if it is regular and edge transitive but not vertex transitive. In this paper we prove that there is no connected cubic semi-symmetric graph of order $12p^3$ for any prime number $p$.