We show that every 7-vertex-connected molecular graph is generically rigid in three dimensions. This verifies a special case of a conjecture of Lovász and Yemini. For this family of graphs the bound is best possible.

Predicating macroscopic influences of drugs on human body, like efficacy and toxicity, is a central problem of smallmolecule based drug discovery. Molecules can be represented as an undirected graph, and we can utilize graph convolution networks to predication molecular properties. However, graph convolutional networks and other graph neural networks all focus on learning node-level representat...

Recently, topology and graph theory have come together to study graphs embedded in 3-space, (see for example [1 5]). An analysis of the symmetries of spatial graphs is useful in chemistry in determining when a molecular bond graph is chiral (i.e., distinct from its mirror image). We are interested in classifying those graphs whose intrinsic structure is such that no matter how they are embedded...

MolNet, a new type of multi-layer feedforward neural network, is presented together with its application to the computation of alkane enthalpies. The MolNet neural network changes its topology (the number of neurons in the input and hidden layers, together with the number and type of connections) according to the molecular structure of the chemical compound presented to the network. The structu...

It is proved that any molecular graph invariant (that is any topological index) can be uniquely represented as (1) a linear combination of occurrence numbers of some substructures (fragments), both connected and disconnected, or (2) a polynomial on occurrence numbers of connected substructures of corresponding molecular graph. Besides, any (0,l)-valued molecular graph invariant can be uniquely ...

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 chemical graph theory, many graph parameters, or topological indices, were proposed as estimators of molecular structural properties. Often several variants of an index are considered. The aim is to extend the original concept to larger families of graphs than initially considered, or to make it more precise and discriminant, or yet to make its range of values similar to that of another inde...

Breast cancer is a complicated disease that it is accompanied by different symptoms. Diagnosis of this disease is performed by various techniques. Using Radiopharmaceuticals is a new method to diagnose the said tumors. [18F]-FPTT is one of these nuclear medicines for detection of breast cancer. It seems that the binding of the title radiopharmaceutical to the progesterone receptor is...

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 $q_8$.