论文标题
$ c_n \ box c_m $的超级标签
Supermagic labeling of $C_n\Box C_m$
论文作者
论文摘要
图$ g（v，e）$ a $ | e | = k $的超级标记（通常也称为超魔牌标签）是从$ e $到第一个$ e $的两组$ k $ pastic Integers，以至于每个verte $ x \ in V $ in Chop $ c $均等于v $的所有事件$ x \等于同一integer $ c $ c $ c $。存在两个循环的笛卡尔产品的超级标签，$ c_ {n} \ box c_m $ for $ n，m \ geq4 $以及$ n，m $偶数，以及任何$ c_n \ box c_n $，带有$ n \ geq3 $的$ n \ box c_n $。 Ivančo还推测，对于任何$ n，m \ geq3 $，对于任何$ c_n \ box c_m $都是可能的。我们证明了他对所有$ n，m $奇数的猜想，这并非相对较好。
A supermagic labeling (often also called supermagic labeling) of a graph $G(V,E)$ with $|E|=k$ is a bijection from $E$ to the set of first $k$ positive integers such that the sum of labels of all incident edges of every vertex $x\in V$ is equal to the same integer $c$. An existence of a supermagic labeling of Cartesian product of two cycles, $C_{n}\Box C_m$ for $n,m\geq4$ and both $n,m$ even and for any $C_n\Box C_n$ with $n\geq3$ was proved by Ivančo. Ivančo also conjectured that such labeling is possible for any $C_n\Box C_m$ with $n,m\geq3$. We prove his conjecture for all $n,m$ odd that are not relatively prime.
