• Corpus ID: 173990950

# $\beta$-Packing Sets in Graphs

@article{Case2019betaPackingSI,
title={\$\beta\$-Packing Sets in Graphs},
author={Benjamin M. Case and Evan Haithcock and Renu C. Laskar},
journal={arXiv: Combinatorics},
year={2019}
}
• Published 31 May 2019
• Mathematics
• arXiv: Combinatorics
A set $S\subseteq V$ is $\alpha$-dominating if for all $v\in V-S$, $|N(v) \cap S | \geq \alpha |N(v)|.$ The $\alpha$-domination number of $G$ equals the minimum cardinality of an $\alpha$-dominating set $S$ in $G$. Since being introduced by Dunbar, et al. in 2000, $\alpha$-domination has been studied for various graphs and a variety of bounds have been developed. In this paper, we propose a new parameter derived by flipping the inequality in the definition of $\alpha$-domination. We say a set…

## References

SHOWING 1-8 OF 8 REFERENCES

### On $$\alpha$$α-Domination in Graphs

• Mathematics
Graphs Comb.
• 2018
Some properties of Sp α (G) are studied and it is shown thatγα(G) changes its value only at rational points as α runs over (0, 1] and some improved probabilistic upper bounds of α are presented.

### Edge-Removal and Edge-Addition in $$\alpha$$α-Domination

• Mathematics
Graphs Comb.
• 2016
G, the graph without isolated vertices, is studied for which the removal of any edge or the addition of any further edge affects the α-domination number of G.

### Fractional Domination, Fractional Packings, and Fractional Isomorphisms of Graphs

Except where reference is made to the work of others, the work described in this dissertation is my own or was done in collaboration with my advisory committee. This dissertation does not include

### Upper Bounds for α-Domination Parameters

• Mathematics, Computer Science
Graphs Comb.
• 2009
A new upper bound is provided for the α-domination number in terms of a parameter α, 0 < α ≤ 1, and graph vertex degrees, which generalises the well-known Caro-Roditty bound for the domination number of a graph.

### ‘Domination’

• Lonnie Athens
• Sociology
The Palgrave Encyclopedia of Imperialism and Anti-Imperialism
• 2021
We owe a great debt to George Herbert Mead for, arguably, analyzing the ‘social act’ more profoundly than anyone else before or after him. While undeniably profound, his analysis, which rests on the

### Some remarks on alpha-domination

• Mathematics, Computer Science
Discuss. Math. Graph Theory
• 2004

• 2016