(1,2)-PDS in graphs with the small number of vertices of large degrees

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 \(n-2\).

Authors

Publication Details

Journal
Opuscula Mathematica
Published
2024-12-20
DOI
https://doi.org/10.7494/opmath.2025.45.1.53
Citations
2
Primary Topic
graph theory and CDMA systems
Type
article
Field-Weighted Citation Impact
0.42
Controls
|||
ALL TIME
JAN
FEB
MAR
APR
MAY
JUN
JUL
AUG
SEP
OCT
article

(1,2)-PDS in graphs with the small number of vertices of large degrees

Urszula Bednarz, Mateusz Pirga
2 citations
Opuscula Mathematica
graph theory and CDMA systems
0.42
article

(1,2)-PDS in graphs with the small number of vertices of large degrees

Urszula Bednarz, Mateusz Pirga
article en
2 citations

Abstract

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 \(n-2\).

Opuscula MathematicaVol. 45(1)
Openalex Percentile: Top 36%
graph theory and CDMA systems
0.42
DOIOpen Access PDFOpenAlex
AI Navigator

Ask Laika to Summarize, Analyze, and Connect papers live on the map.

Summarize Papers & Methodologies

Extract key findings, datasets, and comparative methods across publications.

Benchmark Rankings & Visual Analytics

Rank top research institutions, authors, funders, topics, and journals by Field-Weighted Citation Impact (FWCI) and paper volume with instant charts.

Connect Distant Disciplines

Bridge topological clusters on the map to find hidden collaborative intersections.

(1,2)-PDS in graphs with the small number of vertices of large degrees — Urszula Bednarz, Mateusz Pirga · Opuscula Mathematica (2024) | TGRS Research Map | TGRS