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.

A wide array of central nervous system complications, neurological deficits, and cognitive impairments occur and persist as a result of systemic cancer and cancer treatments. This condition is known as chemo brain and it affects over half of cancer survivors. Recent studies reported that cognitive impairments manifest before chemotherapy and are much broader than chemo brain alone, thereby addi...

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.

The recent advancements in graph neural networks (GNNs) have led to state-of-the-art performances various applications, including chemo-informatics, question-answering systems, and recommender systems. However, scaling up these methods huge graphs, such as social Web remains a challenge. In particular, the existing for accelerating GNNs either are not theoretically guaranteed terms of approxima...

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 ...

BACKGROUND To evaluate the metabolic changes on ¹⁸F-fluoro-2-deoxyglucose positron emission tomography integrated with computed tomography (¹⁸ F-FDG PET-CT) performed before, during and after concurrent chemo-radiotherapy in patients with locally advanced non-small cell lung cancer (NSCLC); to correlate the metabolic response with the delivered radiation dose and with the clinical outcome. ME...

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...

In silico approaches have been widely recognised to be useful for drug discovery. Here, we consider the significance of available databases of medicinal plants and chemo- and bioinformatics tools for in silico drug discovery beyond the traditional use of folk medicines. This review contains a practical example of the application of combined chemo- and bioinformatics methods to study pleiotropic...