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On optimal summable graphs

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

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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 .

Item Type: Journal Article
Publisher: Kalasalingam University
Copyright: (C)2006 Department of Mathematics. Kalasalingam University
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