Conjectures on index and algebraic connectivity of graphs
โ Scribed by Kinkar Ch. Das
- Publisher
- Elsevier Science
- Year
- 2010
- Tongue
- English
- Weight
- 354 KB
- Volume
- 433
- Category
- Article
- ISSN
- 0024-3795
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๐ SIMILAR VOLUMES
In this paper, we investigate how the algebraic connectivity of a connected graph behaves when the graph is perturbed by separating or grafting an edge.
Our purpose is to consider the following conjectures: Conjecture 1 (Barneffe). . Every cubic 3-connected bipartite planar graph is Hamiltonian. Conjecture 2 (Jaeger). Every cubic cyclically 4-edge connected graph G has a cycle C such that G -V(C) is acyclic. Conjecture 3 (Jackson, Fleischner). Ever
We find an upper bound on the algebraic connectivity of graphs of various genus. We begin by showing that for fixed k 1, the graph of genus k of largest algebraic connectivity is a complete graph. We then find an upper bound for noncomplete graphs of a fixed genus k 1 and we determine the values of