单圈图和双圈图的次大次小约化Sombor指标  

Second-Maximum and Second-Minimum Values ofReduced Sombor Index in Unicyclic and Bicyclic Graphs

作　　者：谭欢 赵飚[1] TAN Huan;ZHAO Biao(College of Mathematics and System Science,Xinjiang University,Urumqi 830017,China)

机构地区：[1]新疆大学数学与系统科学学院,乌鲁木齐830017

出　　处：《吉林大学学报(理学版)》2025年第2期382-390,共9页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:12161085);新疆维吾尔自治区自然科学基金(批准号:2021D01C069).

摘　　要：首先,利用图形变换及独特的分类方法解决n(n≥5)阶单圈图的约化Sombor指标最大、次大和次小以及对应的极图问题;其次,考虑n(n≥6)阶双圈图的约化Sombo r指标次大、次小以及对应的极图问题,给出n(n≥5)阶单圈图最大、第二大以及第二小的约化Sombor指标,并刻画对应的极图;同时还确定了n(n≥6)阶双圈图第二大和第二小的约化Sombor指标及所对应的极图.Firstly,we solved the problem of the maximum,second-maximum and second-minimum values of the reduced Sombor index of n(n≥5)order unicyclic graphs,and the corresponding extremal graphs by using graphical transformations and unique classification methods.Secondly,we considered the problems of the second-maximum and second-minimum values of the reduced Sombor index of n(n≥6)order bicyclic graphs,and the corresponding extremal graphs,gave the maximum,second-maximum and second-minimum values of the reduced Sombor index of n(n≥5)order unicyclic graphs,and characterized the corresponding extremal graphs.At the same time,we also confirmed the second-maximum and second-minimum values of the reduced Sombor index of n(n≥6)order bicyclic graphs,and the corresponding extremal graphs.

关 键 词：约化Sombor指标 单圈图 双圈图 极图 

分 类 号：O157.5[理学—数学]