Journal of East China Normal University(Natural Sc ›› 2009, Vol. 2009 ›› Issue (1): 13-21.

• Article • Previous Articles     Next Articles

On dissection of unicyclic graphs(English)

WANG Xiao1, DUAN Fang2   

  1. 1. Department of Mathematics, Shangluo University, Shangluo Shanxi} 726000, China; 2.School of Maths-Physics and Information Science, Xinjiang Normal University, Urumqi 830054, China
  • Received:2008-06-03 Revised:2008-08-20 Online:2009-01-25 Published:2009-01-25
  • Contact: WANG Xiao

Abstract: By the principle of mathematical induction and classified
discussion, the sharp bounds for dissection of unicyclic graphs of a
fixed order were given. Among all unicyclic graphs of order
$n(n\geqslant 6)$, the graph $\Delta_{n-3}$ has the minimum $a(G)$
and $b(G)$, and the graph $K_{1,n-1}^{+}$ has maximum $a(G)$ and
$b(G)$, where $\Delta_{n-3}$ denotes the graph obtained from $K_{3}$
and $P_{n-3}$ by joining a vertex of $K_{3}$ to one endvertex of
$P_{n-3}$, and $K_{1,n-1}^{+}$ denotes the graph obtained from
$K_{1,n-1}$ by joining its two vertices of degree one.

Key words: bound, dissection, unicyclic graphs, bound, dissection

CLC Number: