3 papers
math.CO2024
Effects of edge addition or removal on the nullity of a graph
Ahmet Batal
Lights Out is a game which can be played on any graph . Initially we have a configuration which assigns one of the two states on or off to each vertex. The aim of the game is to…
math.CO2024
Parity of an odd dominating set
Ahmet Batal
For a simple graph with vertex set , we define the closed neighborhood set of a vertex as $N[u]=\{v \in V(G) \; | \; v \; \text{is adjacent to} \; u \…
math.CO2024
A characterization of always solvable trees in the Lights Out game using the activation types of vertices
Ahmet Batal
Lights out is a game that can be played on any simple graph . A configuration assigns one of the two states \emph{on} or \emph{off} to each vertex. For a given configuration, th…