Operations on Nerves

On exponential domination and graph operations

An exponential dominating set of graph $G = (V,E )$ is a subset $Ssubseteq V(G)$ such that $sum_{uin S}(1/2)^{overline{d}{(u,v)-1}}geq 1$ for every vertex $v$ in $V(G)-S$, where $overline{d}(u,v)$ is the distance between vertices $u in S$ and $v  in V(G)-S$ in the graph $G -(S-{u})$. The exponential domination number, $gamma_{e}(G)$, is the smallest cardinality of an exponential dominating set....

2 - Pressure on nerves

On Powers of Some Graph Operations

Let $G*H$ be the product $*$ of $G$ and $H$. In this paper we determine the rth power of the graph $G*H$ in terms of $G^r, H^r$ and $G^r*H^r$, when $*$ is the join, Cartesian, symmetric difference, disjunctive, composition, skew and corona product. Then we solve the equation $(G*H)^r=G^r*H^r$. We also compute the Wiener index and Wiener polarity index of the skew product.

Banach on Linear Operations 13 Banach on Linear Operations

Théorie des Opérations Linéaires. By Stefan Banach. Warsaw, Monografje Matematyczne, Vol. I, 1932. vii+254 pp. The present book, the first of the series published by the Monografje Matematyzcne, is an enlarged and considerably modified translation of the Teorja Operacyi (in Polish) by Banach. It represents a noteworthy climax of long series of researches started by Volterra, Fredholm, Hubert, H...

Comments on “Neuromuscular Ultrasonography of Cranial Nerves”

Comments on " Neuromuscular Ultrasonography of Cranial Nerves " Dear Editor, We read with great interest the review article by Tawfik et al. 1 on the clinical applications of neuromuscular ultrasonography of cranial nerves. We would like to congratulate the authors for their interesting review, but we would also like to make some comments on the section concerning optic nerve (ON) evaluations, ...