S. Fujita

activity

20182022

collaborators

8 papers

math.CO2022

New classification of graphs in view of the domination number of central graphs

Shinya Fujita, Farshad Kazemnejad, Behnaz Pahlavsay

For a graph $G$ , the central graph $C (G)$ is the graph constructed from $G$ by subdividing each edge of $G$ with one vertex and also by adding an edge to every pair of non-adjacent…

math.CO2021

On properly ordered coloring of vertices in a vertex-weighted graph

Shinya Fujita, Sergey Kitaev, Shizuka Sato +1

We introduce the notion of a properly ordered coloring (POC) of a weighted graph, that generalizes the notion of vertex coloring of a graph. Under a POC, if $x y$ is an edge, then t…

math.CO2020

The optimal proper connection number of a graph with given independence number

Shinya Fujita, Boram Park

An edge-colored connected graph $G$ is properly connected if between every pair of distinct vertices, there exists a path that no two adjacent edges have a same color. Fujita (2019…

math.CO2019

The size of graphs with restricted rainbow $2$ -connection number

Shinya Fujita, Henry Liu, Boram Park

Let $k$ be a positive integer, and $G$ be a $k$ -connected graph. An edge-coloured path is \emph{rainbow} if all of its edges have distinct colours. The \emph{rainbow $k$ -connection…

math.CO2019

Stable structure on safe set problems in vertex-weighted graphs

Shinya Fujita, Tadashi Sakuma, Boram Park

Let $G$ be a graph, and let $w$ be a positive real-valued weight function on $V (G)$ . For every subset $S$ of $V (G)$ , let $w (S) = \sum_{v \in S} w (v) .$ A non-empty subset $S \subset V…

cs.CC2019

Safe sets in digraphs

Yandong Bai, Jørgen Bang-Jensen, Shinya Fujita +1

A non-empty subset $S$ of the vertices of a digraph $D$ is called a {\it safe set} if \begin{itemize} \item[(i)] for every strongly connected component $M$ of $D - S$ , there exists a…