论文标题
某些独立图的超级边缘魔术总强度
Super edge-magic total strength of some unicyclic graphs
论文作者
论文摘要
令$ g $为有限的简单无向$（p，q）$ - 图形，带有顶点套装$ v（g）$和edge set $ e（g）$，以便$ p = | v（g）| $和$ q = | e（g）| $。超级边缘杂物总标签$ g $的$ g $是一个双重$ f \ colon v（g）\ cup e（g）\ longrightArrow \ {1,2，\ dots，p+q \} $，使得所有edgges $ u v \ in e（g）$，$ f（u）$ f（u）+f（u）+f（u）+f（f）常数，$ f（v（g））= \ {1，\ dots，p \} $。所有$ c（f）$的最低限度，其中最低限度在所有超级边缘魔法总标签上$ f $ $ g $，定义为图形$ g $的超级边缘魔术总强度。在本文中，我们将处理某些类别的单周期图，并提供大量证据，以猜测某个单轮循环$（p，q）$ - 图形等于$ 2q+\ frac {n+3} {2} $。
Let $G$ be a finite simple undirected $(p,q)$-graph, with vertex set $V(G)$ and edge set $E(G)$ such that $p=|V(G)|$ and $q=|E(G)|$. A super edge-magic total labeling $f$ of $G$ is a bijection $f\colon V(G)\cup E(G)\longrightarrow \{1,2,\dots , p+q\}$ such that for all edges $u v\in E(G)$, $f(u)+f(v)+f(u v)=c(f)$, where $c(f)$ is called a magic constant, and $f(V(G))=\{1,\dots , p\}$. The minimum of all $c(f)$, where the minimum is taken over all the super edge-magic total labelings $f$ of $G$, is defined to be the super edge-magic total strength of the graph $G$. In this article, we work on certain classes of unicyclic graphs and provide shreds of evidence to conjecture that the super edge-magic total strength of a certain family of unicyclic $(p,q)$-graphs is equal to $2q+\frac{n+3}{2}$.
