几类特殊图的符号差  

Signature of Several Special Graphs

作　　者：谢朝阳 何常香[1] 

机构地区：[1]上海理工大学理学院,上海200093

出　　处：《上海理工大学学报》2018年第1期1-4,共4页Journal of University of Shanghai For Science and Technology

基　　金：国家自然科学基金资助项目(11301340)

摘　　要：针对符号差的一个猜想:-c_3(G)≤s(G)≤c_5(G),基于特征值交错定理以及秩和符号差的关系,运用归纳法证明了n阶图G中若存在点v,满足d(v)<n-1且r(G)≠r(G-v)+1,则猜想成立,并以实例说明了满足条件的图类的存在性.同时证明了若图H是k圈图,χ_H为H的核,如果存在点v∈χ_H使得点v是H{v}的可匹配点,则H也满足猜想.There is a conjecture on the signature:-c_3(G)≤s(G)≤c_5(G).Based on the eigenvalue interleaving theorem and the relationship between the rank and the signature,the induction method was used to prove that if there exists a vertex v in Gsatisfying d(v)<n-1 and r(G)≠r(G-v)+1,then the conjecture holds.Furthemore,some examples were given to demonstrate the existence of the mentioned graphs.Meanwhile,it was proved that if His a k-cyclic graph with base χ_H ,if there exists a vertex v on χ_H such that v is matched in H{v},then the graph H also coincides with the conjecture.

关 键 词：图 符号差 K圈图 

分 类 号：O157.5[理学—数学]