On the Roman Bondage Number of Planar Graphs

On the bondage number of a graph

✍ Yue-Li Wang 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 162 KB

The bondage number b(G) of a graph G is the minimum cardinality of a set of edges of G whose removal from G makes the domination number of G increase. There are several papers discussed the upper bound of b(G). In this paper, we shall give an improved upper bound of b(G).

The bondage number of a graph

✍ John Frederick Fink; Michael S. Jacobson; Lael F. Kinch; John Roberts 📂 Article 📅 1990 🏛 Elsevier Science 🌐 English ⚖ 654 KB

Bounds on the bondage number of a graph

✍ Bert L. Hartnell; Douglas F. Rall 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 317 KB

The bondage number b(G) of a graph G is the minimum cardinality of a set of edges of G whose removal from G results in a graph with domination number larger than that of G. Several new sharp upper bounds for b(G) are established. In addition, we present an infinite class of graphs each of whose bond

A counterexample to a conjecture on the

A counterexample to a conjecture on the bondage number of a graph

✍ Ulrich Teschner 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 113 KB

The bondage number h(G) of a nonempty graph G was first introduced by Fink, Jacobson, Kinch and Roberts in [3]. They generalized a former approach to domination-critical graphs, In their publication they conjectured that b(G)<d(G)+ 1 for any nonempty graph G.

Domination numbers of planar graphs

✍ MacGillivray, G.; Seyffarth, K. 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 967 KB

The problem of determining the domination number of a graph is a well known NPhard problem, even when restricted to planar graphs. By adding a further restriction on the diameter of the graph, we prove that planar graphs with diameter two and three have bounded domination numbers. This implies that

Cyclomatic numbers of planar graphs

✍ Klara J. Cohn 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 283 KB

For a given planar graph G with a set A of independent vertices, we provide a best-possible upper bound for the minimum cyclomatic number of connected induced subgraphs of G containing A. The extremal graphs are also characterized. @