IJPAM: Volume 106, No. 2 (2016)

BONDAGE AND STRONG-WEAK BONDAGE NUMBERS OF
TRANSFORMATION GRAPHS $G^{xyz}$

Aysun Aytaç$^1$, Tufan Turaci$^2$
$^1$Department of Mathematics
Faculty of Science
Ege University, 35100, İzmir, TURKEY
$^2$Department of Mathematics
Faculty of Science
Karabük University
78050, Karabük, TURKEY


Abstract. Let $G(V(G),E(G))$ be a simple undirected graph. A dominating set of $G$ is a subset $D\subseteq V(G)$ such that every vertex in $V(G)-D$ is adjacent to at least one vertex in $D$. The minimum cardinality taken over all dominating sets of $G$ is called the domination number of $G$ and also is denoted by $\gamma(G)$. There are a lot of vulnerability parameters depending upon dominating set. These parameters are strong and weak domination numbers, reinforcement number, bondage number, strong and weak bondage numbers, etc. The bondage parameters are important in these parameters. The bondage number $b(G)$ of a nonempty graph $G$ is the cardinality of a smallest set of edges whose removal from $G$ results in a graph with domination number greater than $\gamma(G)$. In this paper, the bondage parameters have been examined of transformation graphs, then exact values and upper bounds have been obtained.

Received: November 6, 2015

AMS Subject Classification: 05C40, 05C69, 68M10, 68R10

Key Words and Phrases: graph vulnerability, connectivity, network design and communication, domination number, strong and weak domination number, bondage number, strong and weak bondage number, transformation graphs

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DOI: 10.12732/ijpam.v106i2.30 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 106
Issue: 2
Pages: 677 - 697


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