残棱柱体模和数的上界

On the Upper Bound of the Sum Number of Incomplete Prism

各种和图标号都可用作图的压缩表示.一个图G称为和图,若它同构于某个SN的和图.一个图G称为模和图,若它同构于某个S{1,2,……,m-1}且所有算术运算均取模m(≥S+1)的和图.图G的模和数ρ(G)是使得G∪ρK1是模和图的非负整数ρ的最小值.Cn×K2称为棱柱体,将棱柱体上下底面的棱Cn进行一次剖分所形成的图形称为残棱柱体.给出了残棱柱体的模和标号,从而证明了残棱柱体的模和数的上界为4.

Sum graph labelling can be used as a compressed representation of a graph by computer. A graph G is said to be a sum graph if it is isomorphic to the sum graph of some S belong to N . A graph G is said to be a mod sum graph if it is isomorphic to the sum graph of some S belong to { 1,2,…… , m - 1 } if all arithmetic is performed modulo m （ ≥ ｜ S ｜ ＋ 1） . The mod sum number ρ （G） of G is the smallest number of isolated vertices which when added to G result in a mod sum graph. Cn × K2 is called prism , it is called incomplete prism when we give a subdivision to Cn of prism . This paper gives a mod sum labelling of incomplete prism, and has proved the upper bound of the sum number of incomplete prism is 4 for all n ≥3.