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On optimal summable graphs
Journal article   Open access   Peer reviewed

On optimal summable graphs

K.M. Koh, M. Miller, W.F. Smyth and Y. Wang
AKCE International Journal of Graphs and Combinatorics, Vol.3(1), pp.45-57
2006
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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 .

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