Toru Araki

collaborators

3 papers

math.CO2024

Secure Total Domination Number in Maximal Outerplanar Graphs

Yasufumi Aita, Toru Araki

A subset $S$ of vertices in a graph $G$ is a secure total dominating set of $G$ if $S$ is a total dominating set of $G$ and, for each vertex $u \neq \in S$ , there is a vertex $v \in…

math.CO2024

A Lower bound for Secure Domination Number of an Outerplanar Graph

Toru Araki

A subset $S$ of vertices in a graph $G$ is a secure dominating set of $G$ if $S$ is a dominating set of $G$ and, for each vertex $u \neq \in S$ , there is a vertex $v \in S$ such tha…

cs.DM2014

On the distance preserving trees in graphs

Toru Araki, Shingo Osawa, Takashi Shimizu

For a vertex $v$ of a graph $G$ , a spanning tree $T$ of $G$ is distance-preserving from $v$ if, for any vertex $w$ , the distance from $v$ to $w$ on $T$ is the same as the distance…