Structural aspects of $1$-limited domination in cubic graphs

@misc{radic2026structural,
  title = {{Structural aspects of $1$-limited domination in cubic graphs}},
  author = {Goran Radić and Gordana Radić and Aleksandra Tepeh},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.26259},
  eprint = {2610.26259},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.26259},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Structural aspects of $1$-limited domination in cubic graphs
AU  - Goran Radić
AU  - Gordana Radić
AU  - Aleksandra Tepeh
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.26259
UR  - https://arxiv.org/abs/2610.26259
AB  - A set D⊆ V(G) is a $1$-limited dominating set of a graph G if every vertex outside D has a neighbor in D and every vertex of D has at most one neighbor outside D. The minimum cardinality among all $1$-limited dominating sets of G is denoted by γ_1^L(G). For every cubic graph G of order n, there exists a nonnegative integer t such that γ_1^L(G)=n/2+t. We establish structural properties of $1$-limited dominating sets in terms of t and use them to study the induced cycles vertex number, that is, the maximum number of vertices inducing a $2$-regular subgraph. As applications, we determine the exact $1$-limited domination numbers of generalized Blanuša snarks and flower snarks.
ER  -