梯子图P_n□P_2的整和数  

The Integral Sum Number of the Ladder Graph P_n□P_2

作　　者：魏建新[1] WEI Jian-xin(School of Mathematics and Statistics Science, Ludong University, Yantai 264025, Chin)

机构地区：[1]鲁东大学数学与统计科学学院,山东烟台264025

出　　处：《数学的实践与认识》2016年第19期178-184,共7页Mathematics in Practice and Theory

基　　金：山东省自然科学基金(ZR2015PA006);鲁东大学博士基金(LY2015006)

摘　　要：Nicholas等人证明梯子图L_n(=P_n□P_2,n≥2)的和数与整和数都是3,并且L_n都是排斥图.结果证明了这个结论是错误的.我们证明了n≥3时,L_n的整和数是0,这就说明n≥3时,所有的L_n的和数与整和数并不相等.还证明当n=3,4,5时,Ln的和数是2,从而它们也不是排斥图.Nicholas et al.proved that both of the sum number and integral sum number of ladder graphs L_n（= P_n□P_2,n≥2） are 3,and all ladder graphs are exclusive.Results in this paper show that their results are wrong.It is proved that for n≥3,the integral sum number of L_n is 0.This indicates that the sum number of In is not equal to the integral sum number of L_n for all n≥3.It is also proved that for n = 3,4 and 5,the sum number of L_n is 2 and so L_n is not exclusive.

关 键 词：梯子图 (整 排斥)和图 (整 排斥)和数 

分 类 号：O157.5[理学—数学]