联积图的超边魔亏
Super edge-magic deficiency of join-product graphs
摘要：
一个图$G$称为\textit{super edge-magic}，如果存在一个从$V(G) \cup E(G)$到$\{1, 2, \ldots, |V(G) \cup E(G)|\}$的双射函数$f$，使得对于$G$的每条边$xy$，$f(V(G)) = \{1, 2, \ldots, |V(G)|\}$和$f(x) + f(xy) + f(y)$都是常数$k$.此外，图$G$的\textit{super edge-magic deficiency}是最小非负整数$n$，使得$G \cup nK_1$是超边幻的，或者是$+\infty$，如果不存在这样的整数.两个图的\emph{Join product}是它们的图并集，其具有将第一个图的所有顶点连接到第二个图的每个顶点的附加边。本文研究了带孤立点的轮减去边和路、星、圈的联积的超边幻亏。
英文摘要：
A graph $G$ is called \textit{super edge-magic} if there exists a bijective function $f$ from $V(G) \cup E(G)$ to $\{1, 2, \ldots, |V(G) \cup E(G)|\}$ such that $f(V(G)) = \{1, 2, \ldots, |V(G)|\}$ and $f(x) + f(xy) + f(y)$ is a constant $k$ for every edge $xy$ of $G$. Furthermore, the \textit{super edge-magic deficiency} of a graph $G$ is either the minimum nonnegative integer $n$ such that $G \cup nK_1$ is super edge-magic or $+\infty$ if there exists no such integer. \emph{Join product} of two graphs is their graph union with additional edges that connect all vertices of the first graph to each vertex of the second graph. In this paper, we study the super edge-magic deficiencies of a wheel minus an edge and join products of a path, a star, and a cycle, respectively, with isolated vertices.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
