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Autor:
Sharafdini, Reza, Reti, Tamas
Publikováno v:
Kragujevac Journal of Mathematics, 44(1) (2020) 44-63
The distance $d(u,v)$ between the vertices $u$ and $v$ of a connected graph $G$ is defined as the number of edges in a minimal path connecting them. The \emph{transmission} of a vertex $v$ of $G$ is defined by $\sigma(v)=\sum\limits_{u\in V(G)}{d(v,u
Externí odkaz:
http://arxiv.org/abs/1710.08176
Let $\Gamma$ be a graph with the adjacency matrix $A$. The energy of $\Gamma$ is the sum of the absolute values of the eigenvalues of $A$. In this article we compute the energies of the commuting graphs of some finite groups and discuss some conseque
Externí odkaz:
http://arxiv.org/abs/1704.06464
The status of a vertex $u$ in a connected graph $G$, denoted by $\sigma_G(u)$, is defined as the sum of the distances between $u$ and all other vertices of a graph $G$. The first and second status connectivity indices of a graph $G$ are defined as $S
Externí odkaz:
http://arxiv.org/abs/1611.08270
Autor:
Sharafdini, Reza, Gutman, Ivan
Publikováno v:
Kragujevac J. Sci. 35 (2013) 89-98
Let $G_1=(V_1,E_1)$ and $G_2=(V_2,E_2)$ be two graphs with disjoint vertex sets $V_1$ and $V_2$. Let $u_1 \in V_1$ and $u_2 \in V_2$. A splice of $G_1$ and $G_2$ by vertices $u_1$ and $u_2$, $\mathcal{S}(G_1,G_2;u_1,u_2)$, is defined by identifying t
Externí odkaz:
http://arxiv.org/abs/1611.02819
Autor:
Sharafdini, Reza, Panahbar, H.
Publikováno v:
Journal of Mathematical Nanoscience, (6) 2016, 49-57
Let $G$ be a graph with a vertex weight $\omega$ and the vertices $v_1,\ldots,v_n$. The Laplacian matrix of $G$ with respect to $\omega$ is defined as $L_\omega(G)=\mathrm{diag}(\omega(v_1),\cdots,\omega(v_n))-A(G)$, where $A(G)$ is the adjacency mat
Externí odkaz:
http://arxiv.org/abs/1609.01425
The energy of a graph $G$ is equal to the sum of the absolute values of the eigenvalues of $G$ , which in turn is equal to the sum of the singular values of the adjacency matrix of $G$. Let $X$, $Y$ and $Z$ be matrices, such that $X+Y= Z$. The Ky Fan
Externí odkaz:
http://arxiv.org/abs/1608.07939
Autor:
Dobrynin, Andrey A., Sharafdini, Reza
Publikováno v:
In Applied Mathematics and Computation 15 April 2020 371
Autor:
Sharafdini, Reza, Hirasaka, Mitsugu
Let $G$ be a group acting faithfully and transitively on $\Omega_i$ for $i=1,2$. A famous theorem by Burnside implies the following fact: If $|\Omega_1|=|\Omega_2|$ is a prime and the rank of one of the actions is greater than two, then the actions a
Externí odkaz:
http://arxiv.org/abs/1309.3725
Autor:
Hirasaka, Mitsugu, Sharafdini, Reza
Publikováno v:
J. Algebra (2010), doi:10.1016/j.jalgebra.2010.05.015
Let $G$ be a group acting on a finite set $\Omega$. Then $G$ acts on $\Omega\times \Omega$ by its entry-wise action and its orbits form the basis relations of a coherent configuration (or shortly scheme). Our concern is to consider what follows from
Externí odkaz:
http://arxiv.org/abs/1002.0628