Permutability graphs of subgroups of some finite non-abelian groups

In this paper, we study the structure of the permutability graphs of subgroups, and the permutability graphs of non-normal subgroups of the following groups: the dihedral groups $D_n$, the generalized quaternion groups $Q_n$, the quasi-dihedral groups $QD_{2^n}$ and the modular groups $M_{p^n}$. Further, we investigate the number of edges, degrees of the vertices, independence number, dominating number, clique number, chromatic number, weakly perfectness, Eulerianness, Hamiltonicity of these graphs.Comment: 35 pages, 1 figur

Classification of finite groups with toroidal or projective-planar permutability graphs

Let $G$ be a group. The permutability graph of subgroups of $G$, denoted by $\Gamma(G)$, is a graph having all the proper subgroups of $G$ as its vertices, and two subgroups are adjacent in $\Gamma(G)$ if and only if they permute. In this paper, we classify the finite groups whose permutability graphs are toroidal or projective-planar. In addition, we classify the finite groups whose permutability graph does not contain one of $K_{3,3}$, $K_{1,5}$, $C_6$, $P_5$, or $P_6$ as a subgraph.Comment: 30 pages, 8 figure

Assessing the Neuronal Serotonergic Target-based Antidepressant Stratagem: Impact of In Vivo Interaction Studies and Knockout Models

Depression remains a challenge in the field of affective neuroscience, despite a steady research progress. Six out of nine basic antidepressant mechanisms rely on serotonin neurotransmitter system. Preclinical studies have demonstrated the significance of serotonin receptors (5-HT1-3,6,7), its signal transduction pathways and classical down stream targets (including neurotrophins, neurokinins, other peptides and their receptors) in antidepressant drug action. Serotonergic control of depression embraces the recent molecular requirements such as influence on proliferation, neurogenesis, plasticity, synaptic (re)modeling and transmission in the central nervous system. The present progress report analyses the credibility of each protein as therapeutically relevant target of depression. In vivo interaction studies and knockout models which identified these targets are foreseen to unearth new ligands and help them transform to drug candidates. The importance of the antidepressant assay selection at the preclinical level using salient animal models/assay systems is discussed. Such test batteries would definitely provide antidepressants with faster onset, efficacy in resistant (and co-morbid) types and with least adverse effects. Apart from the selective ligands, only those molecules which bring an overall harmony, by virtue of their affinities to various receptor subtypes, could qualify as effective antidepressants. Synchronised modulation of various serotonergic sub-pathways is the basis for a unique and balanced antidepressant profile, as that of fluoxetine (most exploited antidepressant) and such a profile may be considered as a template for the upcoming antidepressants. In conclusion, 5-HT based multi-targeted antidepressant drug discovery supported by in vivo interaction studies and knockout models is advocated as a strategy to provide classic molecules for clinical trials