The Nullities of Signed Cycle-Spliced Graphs  

作　　者：Sarula CHANG Jianxi LI Yirong ZHENG 

机构地区：[1]College of Science,Inner Mongolia Agricultural University,Inner Mongolia 010018,P.R.China [2]School of Mathematics and Statistics,Minnan Normal University,Fujian 363000,P.R.China [3]School of Mathematics and Statistics,Xiamen University of Technology,Fujian 361000,P.R.China

出　　处：《Journal of Mathematical Research with Applications》2023年第6期631-647,共17页数学研究及应用（英文版）

基　　金：Supported by the Natural Science Foundation of Inner Mongolia Autonomous Region(Grant No.2020BS01011);the National Natural Science Foundation of China(Grant No.12171089);the Natural Science Foundation of Fujian Province(Grant No.2021J02048);the Research Fund of Xiamen University of Technology(Grant Nos.YKJ20018R,XPDKT20039)。

摘　　要：Letη(Γ)and c(Γ)be the nullity and the cyclomatic number of a signed graphΓ.A signed cycle-spliced graph is a connected signed graph in which every block is a cycle.In this paper,we prove that for every signed cycle-spliced graphΓ,η(Γ)≤c(Γ)+1 and the extremal graphsΓwith nullity c(Γ)+1 are characterized,which extend the related results of Wong,Zhou and Tian(2022)on simple cycle-spliced graphs.Moreover,we prove that for every signed cycle-spliced graphΓ,η(Γ)=/c(Γ).Some properties on signed cycle-spliced graphsΓwithη(Γ)=c(Γ)-1 are explored,as well as a structural characterization on signed cycle-spliced bipartite graphsΓsatisfyingη(Γ)=c(Γ)-1.

关 键 词：signed graph NULLITY cyclomatic number 

分 类 号：O157.5[理学—数学]