let $r$ be a ring with unity. the undirected nilpotent graph of $r$, denoted by $gamma_n(r)$, is a graph with vertex set ~$z_n(r)^* = {0neq x in r | xy in n(r) for some y in r^*}$, and two distinct vertices $x$ and $y$ are adjacent if and only if $xy in n(r)$, or equivalently, $yx in n(r)$, where $n(r)$ denoted the nilpotent elements of $r$. recently, it has been proved that if $r$ is a left ar...

given a non-abelian finite group $g$, let $pi(g)$ denote the set of prime divisors of the order of $g$ and denote by $z(g)$ the center of $g$. thetextit{ prime graph} of $g$ is the graph with vertex set $pi(g)$ where two distinct primes $p$ and $q$ are joined by an edge if and only if $g$ contains an element of order $pq$ and the textit{non-commuting graph} of $g$ is the graph with the vertex s...

In this paper, an analytical formula to calculate the radial stiffness of groove elastic support is presented. The influence of structure parameters on radial stiffness and homogeneity of radial stiffness is investigated as well. The accuracy and calculating speed of the analysis formula are compared to that of finite element method (FEM). Findings are as following: The calculating speed of ana...

let $g$ be a non-abelian finite group. in this paper, we prove that $gamma(g)$ is $k_4$-free if and only if $g cong a times p$, where $a$ is an abelian group, $p$ is a $2$-group and $g/z(g) cong mathbb{ z}_2 times mathbb{z}_2$. also, we show that $gamma(g)$ is $k_{1,3}$-free if and only if $g cong {mathbb{s}}_3,~d_8$ or $q_8$.

we define minimal cn-dominating graph $mathbf {mcn}(g)$, commonality minimal cn-dominating graph $mathbf {cmcn}(g)$ and vertex minimal cn-dominating graph $mathbf {m_{v}cn}(g)$, characterizations are given for graph $g$ for which the newly defined graphs are connected. further serval new results are developed relating to these graphs.

In this paper, we enumerate the parameter matrices of all perfect $2$-colorings of the Platonic graphs consisting of the tetrahedral graph, the cubical graph, the octahedral graph, the dodecahedral graph, and  the icosahedral graph.

a signed graph (marked graph) is an ordered pair $s=(g,sigma)$$(s=(g,mu))$, where $g=(v,e)$ is a graph called the underlyinggraph of $s$ and $sigma:erightarrow{+,-}$$(mu:vrightarrow{+,-})$ is a function. for a graph $g$, $v(g),e(g)$ and $c(g)$ denote its vertex set, edge set and cut-vertexset, respectively. the lict graph $l_{c}(g)$ of a graph $g=(v,e)$is defined as the graph having vertex set ...

In radial basis function (RBF) networks, placement of centers is said to have a significant effect on the performance of the network. Supervised learning of center locations in some applications show that they are superior to the networks whose centers are located using unsupervised methods. But such networks can take the same training time as that of sigmoid networks. The increased time needed...

Convolutional Radial Basis Function (RBF) networks are introduced for smoothing out irregularly sampled signals. Our proposed technique involves training a RBF network and then convolving it with a Gaussian smoothing kernel in an analytical manner. Since the convolution results in an analytic form, the computation necessary for numerical convolution is avoided. Convolutional RBF networks need t...

let $g$ be a group. the order graph of $g$ is the (undirected)graph $gamma(g)$,those whose vertices are non-trivial subgroups of $g$ and two distinctvertices $h$ and $k$ are adjacent if and only if either$o(h)|o(k)$ or $o(k)|o(h)$. in this paper, we investigate theinterplay between the group-theoretic properties of $g$ and thegraph-theoretic properties of $gamma(g)$. for a finite group$g$, we s...