扩张的不规则性与Pell图
Irregularity of expansions and Pell graphs
摘要：
对于图$G$，$G$的边$uv$的不平衡是$|deg_G(u)-deg_G(v)|$。图$G$的不规则性被定义为在图$G$的所有边上的不平衡之和。在本文中，我们考虑扩展和佩尔图。如果$H$是$G$关于集合$V_1$和$V_2$的扩展，我们用$G, V_1$和$V_2$表示$H$的不规则性。研究了Pell图的边不平衡性。给出了具有固定不平衡度$k$的Pell图的边数.利用这些结果给出了Pell图的无规则性和$σ$ -指数.
英文摘要：
For a graph $G$ the imbalance of an edge $uv$ of $G$ is $|deg_G(u)-deg_G(v)|$. Irregularity of a graph $G$ is defined as the sum of imbalances over all edges of $G$. In this paper we consider expansions and Pell graphs. If $H$ is an expansion of $G$ with respect to the sets $V_1$ and $V_2$, we express the irregularity of $H$ using $G, V_1$ and $V_2$. For Pell graphs the imbalance of their edges is studied. The number of edges of a Pell graph with a fixed imbalance $k$ is expressed. Using these results the irregularity and the $σ$-index of Pell graphs are given.
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