Extending connectivity functions on R n ✩

Extending Connectivity Functions on R

A function f : R → R is a connectivity function if for every connected subset C of R the graph of the restriction f |C is a connected subset of R, and f is an extendable connectivity function if f can be extended to a connectivity function g : R → R with R imbedded into R as R × {0}. There exists a connectivity function f : R → R that is not extendable. We prove that for n ≥ 2 every connectivit...

Extending Functions in the Model Subspaces of H^2(R) to C

Eccentric Connectivity and Augmented Eccentric Connectivity Indices of N-Branched Phenylacetylenes Nanostar Dendrimers

Tricyclic and Tetracyclic Graphs with Maximum and Minimum Eccentric Connectivity

Let $G$ be a connected graph on $n$ vertices. $G$ is called tricyclic if it has $n + 2$ edges, and tetracyclic if $G$ has exactly $n + 3$ edges. Suppose $mathcal{C}_n$ and $mathcal{D}_n$ denote the set of all tricyclic and tetracyclic $n-$vertex graphs, respectively. The aim of this paper is to calculate the minimum and maximum of eccentric connectivity index in $mathcal{C}_n$ and $mathcal{D}_n...

Linear Functions Preserving Sut-Majorization on RN

Suppose $textbf{M}_{n}$ is the vector space of all $n$-by-$n$ real matrices, and let $mathbb{R}^{n}$ be the set of all $n$-by-$1$ real vectors. A matrix $Rin textbf{M}_{n}$ is said to be $textit{row substochastic}$ if it has nonnegative entries and each row sum is at most $1$. For $x$, $y in mathbb{R}^{n}$, it is said that $x$ is $textit{sut-majorized}$ by $y$ (denoted by $ xprec_{sut} y$) if t...