TY  - JOUR
ID  - Bednarz2025
LB  - Bednarz2025
AU  - Bednarz, Urszula
AU  - Pirga, Mateusz
TI  - (1,2)-PDS in graphs with the small number of vertices of large degrees
ST  - (1,2)-PDS in graphs with the small number of vertices of large degrees
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2025
VL  - 45
IS  - 1
SP  - 53
EP  - 62
DO  - https://doi.org/10.7494/OpMath.2025.45.1.53
UR  - https://doi.org/10.7494/OpMath.2025.45.1.53
AB  - We define and study a perfect \((1,2)\)-dominating set which is a special case of a \((1,2)\)-dominating set. We discuss the existence of a perfect \((1,2)\)-dominating set in graphs with at most two vertices of maximum degree. In particular, we present a complete solution if the maximum degree equals \(n-1\) or \(n-2\).
KW  - domination
KW  - secondary domination
KW  - neighborhoods
KW  - maximum degree
SN  - 1232-9274
ER  -