DOAJ Open Access 2016

Heredity for generalized power domination

Paul Dorbec Seethu Varghese Ambat Vijayakumar

Lihat Sumber DOI

Abstrak

In this paper, we study the behaviour of the generalized power domination number of a graph by small changes on the graph, namely edge and vertex deletion and edge contraction. We prove optimal bounds for $\gamma_{p,k}(G-e)$, $\gamma_{p,k}(G/e)$ and for $\gamma_{p,k}(G-v)$ in terms of $\gamma_{p,k}(G)$, and give examples for which these bounds are tight. We characterize all graphs for which $\gamma_{p,k}(G-e) = \gamma_{p,k}(G)+1$ for any edge $e$. We also consider the behaviour of the propagation radius of graphs by similar modifications.

Topik & Kata Kunci

Mathematics

Penulis (3)

Paul Dorbec

Seethu Varghese

Ambat Vijayakumar

Format Sitasi

APA MLA BibTeX

Dorbec, P., Varghese, S., Vijayakumar, A. (2016). Heredity for generalized power domination. https://doi.org/10.46298/dmtcs.1290

Akses Cepat

Lihat di Sumber doi.org/10.46298/dmtcs.1290

Informasi Jurnal

Tahun Terbit: 2016
Sumber Database: DOAJ
DOI: 10.46298/dmtcs.1290
Akses: Open Access ✓