Repository logo

Browsing by Subject "corona"

Filter results by typing the first few letters
Now showing 1 - 2 of 2
  • thumbnail.journal.alt
    Item type:Article, Access status: Open Access ,
    Introduction to dominated edge chromatic number of a graph
    (Wydawnictwa AGH, 2021) Piri, Mohammad R.; Alikhani, Saeid
    We introduce and study the dominated edge coloring of a graph. A dominated edge coloring of a graph $G$, is a proper edge coloring of $G$ such that each color class is dominated by at least one edge of $G$. The minimum number of colors among all dominated edge coloring is called the dominated edge chromatic number, denoted by $\chi_{dom}^{\prime}(G)$. We obtain some properties of $\chi_{dom}^{\prime}(G)$ and compute it for specific graphs. Also examine the effects on $\chi_{dom}^{\prime}(G)$, when $G$ is modified by operations on vertex and edge of $G$. Finally, we consider the $k$-subdivision of $G$ and study the dominated edge chromatic number of these kind of graphs.
  • thumbnail.journal.alt
    Item type:Article, Access status: Open Access ,
    Spectra of subnormal pairs
    (2007) Rudol, Krzysztof
    In this short note we present an example related to joint spectra of subnormal pairs of bounded operators. A counterexample to the equality between Taylor's spectrum and the closure of the defect spectrum is given. This example is related to the author's modification of N Sibony's counterexample to Corona Theorem on domains that fail to be strictly pseudoconvex.