IJPAM: Volume 35, No. 2 (2007)

CONSTRUCTION OF $2$-CONNECTED
$k$-REGULAR SIMPLE GRAPHS

Jing-Rong Chen$^1$, Jian-Ning Yu$^2$
$^{1,2}$College of Mathematics, Physics and Software Engineering
Lanzhou Jiaotong University
Lanzhou, 730070, P.R. CHINA
$^1$e-mail: jdlbxx@mail.lzjtu.cn


Abstract.The construction of 2-connected $k$-regular simple graphs is obtained in this paper. According to two situations of $n=5l$ $(l\geq 1)$ and $n=5l+t$ $(t=1,2,3,4)$, we give the construction procedures when $k=4$, where $n$ denotes the vertex number of graph $G_n$. Then the methods are extended to $k=2m$ and $k=2m+1$ $(m\geq 1)$.

Received: December 11, 2006

AMS Subject Classification: 05C15, 68R10, 94C15

Key Words and Phrases: regular graph, connected graph, union of graph, construction

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 35
Issue: 2