如果两个符号图中的一个与另一个的交换同构，则称这两个符号图是交换同构的。轮$W_n$是循环$C_n$和顶点的连接。对于$0 \leq p \leq n$，$ψ_{p}(n)$被定义为在$C_n$上具有恰好$p$负边缘的交换非同构有符号$W_n$的数目。交换非同构带符号$W_n$的数目由$ψ(n)$表示。本文计算了$p=0,1,2,3,4,n-4,n-3,n-2,n-1,n$的$ψ_{p}(n)$值和$n=4,5,...,10$的$ψ(n)$值。我们的方法获得$ψ_{p}(n)$不仅计数开关非同构符号轮，但也产生他们。
英文摘要：
Two signed graphs are called switching isomorphic to each other if one is isomorphic to a switching of the other. The wheel $W_n$ is the join of the cycle $C_n$ and a vertex. For $0 \leq p \leq n$, $ψ_{p}(n)$ is defined to be the number of switching non-isomorphic signed $W_n$ with exactly $p$ negative edges on $C_n$. The number of switching non-isomorphic signed $W_n$ is denoted by $ψ(n)$. In this paper, we compute the values of $ψ_{p}(n)$ for $p=0,1,2,3,4,n-4,n-3,n-2,n-1,n$ and of $ψ(n)$ for $n=4,5,...,10$. Our method of obtaining $ψ_{p}(n)$ not only count the switching non-isomorphic signed wheels but also generates them.
Signed Counting on Restricted Partitions and Combinatorial Proofs of Three Identities
College of Mathematics and Statistics & Center for Discrete Mathematics, Chongqing University（重庆大学数学与统计学院与离散数学中心）；College of Mathematics and Statistics, Chongqing University（重庆大学数学与统计学院）
Small Ramsey numbers for books, wheels, and generalizations
Iowa State University（爱荷华州立大学）；Center for Communications Research, La Jolla（拉霍亚通信研究中心）；University of Colorado Denver（科罗拉多大学丹佛分校）；Ghent University（根特大学）
