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

The complement of proper power graphs of finite groups

For a finite group $G$, the proper power graph $\mathscr{P}^*(G)$ of $G$ is the graph whose vertices are non-trivial elements of $G$ and two vertices $u$ and $v$ are adjacent if and only if $u \neq v$ and $u^m=v$ or $v^m=u$ for some positive integer $m$. In this paper, we consider the complement of $\mathscr{P}^*(G)$, denoted by ${\overline{\mathscr{P}^*(G)}}$. We classify all finite groups whose complement of proper power graphs is complete, bipartite, a path, a cycle, a star, claw-free, triangle-free, disconnected, planar, outer-planar, toroidal, or projective. Among the other results, we also determine the diameter and girth of the complement of proper power graphs of finite groups.Comment: 29 pages, 14 figures, Lemma 4.1 has been added and consequent changes have been mad

Novel Molecules for Intra-Oral Delivery of Antimicrobials to Prevent and Treat Oral Infectious Diseases

New molecules were designed for efficient intra-oral delivery of antimicrobials to prevent and treat oral infection. The salivary statherin fragment, which has high affinity for the tooth enamel, was used as a carrier peptide. This was linked through the side chain of the N-terminal residue to the C-terminus of a defensin-like 12-residue peptide to generate two bifunctional hybrid molecules, one with an ester linkage and the other with an anhydride bond between the carrier and the antimicrobial components. They were examined for their affinity to a HAP (hydroxyapatite) surface. The extent of the antimicrobial release in human whole saliva was determined using 13C-NMR spectroscopy. The candidacidal activity of the molecules was determined as a function of the antimicrobial release from the carrier peptide in human saliva. The hybrid-adsorbed HAP surface was examined against Candida albicans and Aggregatibacter actinomycetemcomitans using the fluorescence technique. The bifunctional molecules were tested on human erythrocytes, GECs (gingival epithelial cells) and GFCs (gingival fibroblast cells) for cytotoxicity. They were found to possess high affinity for the HAP mineral. In human whole saliva, a sustained antimicrobial release over a period of more than 40–60 h, and candidacidal activity consistent with the extent of hybrid dissociation were observed. Moreover, the bifunctional peptide-bound HAP surface was found to exhibit antimicrobial activity when suspended in clarified human saliva. The hybrid peptides did not show any toxic influence on human erythrocytes, GECs and GFCs. These novel hybrids could be safely used to deliver therapeutic agents intra-orally for the treatment and prevention of oral infectious diseases

Continuous maintenance and the future – Foundations and technological challenges

High value and long life products require continuous maintenance throughout their life cycle to achieve required performance with optimum through-life cost. This paper presents foundations and technologies required to offer the maintenance service. Component and system level degradation science, assessment and modelling along with life cycle ‘big data’ analytics are the two most important knowledge and skill base required for the continuous maintenance. Advanced computing and visualisation technologies will improve efficiency of the maintenance and reduce through-life cost of the product. Future of continuous maintenance within the Industry 4.0 context also identifies the role of IoT, standards and cyber security