A graph $G$ is called \textit{super edge-magic} if there exists a bijectivefunction $f$ from $V(G) \cup E(G)$ to $\{1, 2, \ldots, |V(G) \cup E(G)|\}$ suchthat $f(V(G)) = \{1, 2, \ldots, |V(G)|\}$ and $f(x) + f(xy) + f(y)$ is aconstant $k$ for every edge $xy$ of $G$. Furthermore, the \textit{superedge-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 nosuch integer. \emph{Join product} of two graphs is their graph union with additional edgesthat connect all vertices of the first graph to each vertex of the secondgraph. In this paper, we study the super edge-magic deficiencies of a wheelminus an edge and join products of a path, a star, and a cycle, respectively,with isolated vertices.
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机译：如果存在从$ V（G）\ cup E（G）$到$ \ {1,2，\ ldots，| V（$（））的双射函数$ f $，则图$ G $被称为\ textit {super edge-magic}。 G）\ cup E（G）| \} $这样$ f（V（G））= \ {1，2，\ ldots，| V（G）| \} $和$ f（x）+ f（xy ）+ f（y）$是$ G $的每个边$ xy $的常数$ k $。此外，图$ G $的\ textit {superedge-magic不足}是最小非负整数$ n $，例如$ G \ cup nK_1 $是super edge-magic或$ + \ infty $（如果不存在这样的整数） 。两个图的\ emph {Join product}是它们的图联合，带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。在本文中，我们研究了车轮减去边缘后的超边缘魔术缺陷，并分别将路径，星形和循环的乘积与孤立的顶点连接起来。
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