Journal article
On optimal summable graphs
AKCE International Journal of Graphs and Combinatorics, Vol.3(1), pp.45-57
2006
Abstract
For a graph G , let σ ( G ) and δ ( G ) denote, respectively, its sum number and minimum degree. Trivially, σ ( G ) ≥ δ ( G ) . A nontrivial connected graph G is called a k -optimum summable graph , where k ≥ 1 , if σ ( G ) = δ ( G ) = k . In this paper, we show that if G is a k -optimum summable graph of order n , k ≥ 3 , then (1) n ≥ 2 k ; (2) the complete bipartite graph K k,n − k is not a spanning subgraph of G . We also describe new families of k -optimum summable graphs for k ≥ 1 .
Details
- Title
- On optimal summable graphs
- Authors/Creators
- K.M. Koh (Author/Creator)M. Miller (Author/Creator)W.F. Smyth (Author/Creator)Y. Wang (Author/Creator)
- Publication Details
- AKCE International Journal of Graphs and Combinatorics, Vol.3(1), pp.45-57
- Publisher
- Kalasalingam University
- Identifiers
- 991005540706007891
- Copyright
- (C)2006 Department of Mathematics. Kalasalingam University
- Murdoch Affiliation
- Murdoch University
- Language
- English
- Resource Type
- Journal article
- Publisher URL
- http://www.akcejournal.org/index.html
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