Groups all of whose undirected Cayley graphs are integral

Let $G$ be a finite group, $S\subseteq G\setminus\{1\}$ be a set such that if $a\in S$, then $a^{-1}\in S$, where $1$ denotes the identity element of $G$. The undirected Cayley graph $Cay(G,S)$ of $G$ over the set $S$ is the graph whose vertex set is $G$ and two vertices $a$ and $b$ are adjacent whenever $ab^{-1}\in S$. The adjacency spectrum of a graph is the multiset of all eigenvalues of the adjacency matrix of the graph. A graph is called integral whenever all adjacency spectrum elements are integers. Following Klotz and Sander, we call a group $G$ Cayley integral whenever all undirected Cayley graphs over $G$ are integral. Finite abelian Cayley integral groups are classified by Klotz and Sander as finite abelian groups of exponent dividing $4$ or $6$. Klotz and Sander have proposed the determination of all non-abelian Cayley integral groups. In this paper we complete the classification of finite Cayley integral groups by proving that finite non-abelian Cayley integral groups are the symmetric group $S_{3}$ of degree $3$, $C_{3} \rtimes C_{4}$ and $Q_{8}\times C_{2}^{n}$ for some integer $n\geq 0$, where $Q_8$ is the quaternion group of order $8$.Comment: Title is change

Distance-regular Cayley graphs with small valency

We consider the problem of which distance-regular graphs with small valency are Cayley graphs. We determine the distance-regular Cayley graphs with valency at most $4$, the Cayley graphs among the distance-regular graphs with known putative intersection arrays for valency $5$, and the Cayley graphs among all distance-regular graphs with girth $3$ and valency $6$ or $7$. We obtain that the incidence graphs of Desarguesian affine planes minus a parallel class of lines are Cayley graphs. We show that the incidence graphs of the known generalized hexagons are not Cayley graphs, and neither are some other distance-regular graphs that come from small generalized quadrangles or hexagons. Among some ``exceptional'' distance-regular graphs with small valency, we find that the Armanios-Wells graph and the Klein graph are Cayley graphs.Comment: 19 pages, 4 table

Study of cavities in a creep crack growth test specimen

Small Angle Neutron Scattering (SANS) and Scanning Electron Microscopy (SEM) have been used to determine the degree of cavitation damage, of length scale 5-300 nm, associated with a creep crack grown in a compact tension specimen cut from a Type 316H stainless steel weldment. The specimen was supplied by EDF Energy as part of an extensive study of creep crack growth in the heat affected zone of reactor components. The creep crack propagates along a line 1.5 mm away from, and parallel to, the weld fusion line boundary before deviating away into parent material. The SANS results show a systematic increase in fractional size distribution of cavities approaching the crack, along lines normal to the crack line, and along lines parallel to the crack line approaching the crack mouth. Both SANS and quantitative metallography measurements using SEM indicate two populations of cavities: smaller cavities of less than 100 nm size having a mean diameter of about 60 nm, and a population of larger cavities of 100-300 nm size with a mean diameter of about 200 nm

Neumaier Cayley graphs

A Neumaier graph is a non-complete edge-regular graph with the property that it has a regular clique. In this paper, we study Neumaier Cayley graphs. We give a necessary and sufficient condition under which a Neumaier Cayley graph is a strongly regular Neumaier Cayley graph. We also characterize Neumaier Cayley graphs with small valency at most $10$.Comment: 17 pages, 1 figur

Acute colonic pseudo-obstruction in an infant after retroperitoneal pyeloplasty successfully treated with rectal irrigation

AbstractAcute colonic pseudo-obstruction is frequently observed in adults but is rarely seen in children. The illness has never been reported in infants, who might differ in their reaction to the acute bowel distension and their response to the available management options. This report describes the presentation of acute colonic pseudo-obstruction in an infant after retroperitoneal pyeloplasty and its successful treatment with rectal irrigation

Fuzzy logic control for energy saving in autonomous electric vehicles

Limited battery capacity and excessive battery dimensions have been two major limiting factors in the rapid advancement of electric vehicles. An alternative to increasing battery capacities is to use better: intelligent control techniques which save energy on-board while preserving the performance that will extend the range with the same or even smaller battery capacity and dimensions. In this paper, we present a Type-2 Fuzzy Logic Controller (Type-2 FLC) as the speed controller, acting as the Driver Model Controller (DMC) in Autonomous Electric Vehicles (AEV). The DMC is implemented using realtime control hardware and tested on a scaled down version of a back to back connected brushless DC motor setup where the actual vehicle dynamics are modelled with a Hardware-In-the-Loop (HIL) system. Using the minimization of the Integral Absolute Error (IAE) has been the control design criteria and the performance is compared against Type-1 Fuzzy Logic and Proportional Integral Derivative DMCs. Particle swarm optimization is used in the control design. Comparisons on energy consumption and maximum power demand have been carried out using HIL system for NEDC and ARTEMIS drive cycles. Experimental results show that Type-2 FLC saves energy by a substantial amount while simultaneously achieving the best IAE of the control strategies tested