19 citations · 21 across the 13 of their papers we have counts for
13 papers · 1 filter
New classification of graphs in view of the domination number of central graphs
Shinya Fujita, Farshad Kazemnejad, Behnaz Pahlavsay
For a graph , the central graph is the graph constructed from by subdividing each edge of with one vertex and also by adding an edge to every pair of non-adjacent…
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 is an edge, then t…
The optimal proper connection number of a graph with given independence number
Shinya Fujita, Boram Park
An edge-colored connected graph 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…
The size of graphs with restricted rainbow -connection number
Shinya Fujita, Henry Liu, Boram Park
Let be a positive integer, and be a -connected graph. An edge-coloured path is \emph{rainbow} if all of its edges have distinct colours. The \emph{rainbow -connection…
Stable structure on safe set problems in vertex-weighted graphs
Shinya Fujita, Tadashi Sakuma, Boram Park
Let be a graph, and let be a positive real-valued weight function on . For every subset of , let A non-empty subset $S \subset V…
Optimal proper connection of graphs
Shinya Fujita
An edge-colored graph is called properly colored if no two adjacent edges share a color in . An edge-colored connected graph is called properly connected if between ever…
On the weighted safe set problem on paths and cycles
Shinya Fujita, Tommy Jensen, Boram Park +1
Let be a graph, and let be a weight function on the vertices of . For every subset of , let A non-empty subset…
On sufficient conditions for rainbow cycles in edge-colored graphs
Shinya Fujita, Bo Ning, Chuandong Xu +1
Let be an edge-colored graph. We use and to denote the number of edges of and the number of colors appearing on , respectively. For a vertex …
Kernels by properly colored paths in arc-colored digraphs
Yandong Bai, Shinya Fujita, Shenggui Zhang
A {\em kernel by properly colored paths} of an arc-colored digraph is a set of vertices of such that (i) no two vertices of are connected by a properly colored dire…
Decomposing edge-colored graphs under color degree constraints
Ruonan Li, Shinya Fujita, Guanghui Wang
For an edge-colored graph , the minimum color degree of means the minimum number of colors on edges which are adjacent to each vertex of . We prove that if is an edge…
Bounding the distance among longest paths in a connected graph
Jan Ekstein, Shinya Fujita, Adam Kabela +1
It is easy to see that in a connected graph any 2 longest paths have a vertex in common. For k>=7, Skupien in [7] obtained a connected graph in which some k longest paths have no c…
A New Approach Towards a Conjecture on Intersecting Three Longest Paths
Shinya Fujita, Michitaka Furuya, Reza Naserasr +1
In 1966, T. Gallai asked whether every connected graph has a vertex that appears in all longest paths. Since then this question has attracted much attention and many work has been…
Partitioning a graph into highly connected subgraphs
Valentin Borozan, Michael Ferrara, Shinya Fujita +4
Given , a -proper partition of a graph is a partition of such that each part of induces a -connected subgraph of . We…