On plane graphs with link component number equal to the nullity
Noble, S. D.
- 数学科学－已发表论文 
In this paper, we study connected plane graphs with link component number equal to the nullity and call them near-extremal graphs. We first study near-extremal graphs with minimum degree at least 3 and prove that a connected plane graph G with minimum degree at least 3 is a near-extremal graph if and only if G is isomorphic to K-4, the complete graph with 4 vertices. The result is obtained by studying general graphs using the knowledge of bicycle space and the Tutte polynomial. Then a simple algorithm is given to judge whether a connected plane graph is a near-extremal graph or not. Finally we study the construction of near-extremal graphs and prove that all near-extremal graphs can be constructed from a loop and K-4 by two graph operations. (C) 2011 Elsevier B.V. All rights reserved.
CitationDISCRETE APPLIED MATHEMATICS，2012,160（9）：1369-1375