{"title":"Enumeration of Labeled Bi-Block Graphs","authors":"V. A. Voblyi","doi":"10.1134/S1990478923040178","DOIUrl":null,"url":null,"abstract":"<p> A bi-block graph is a connected graph in which all blocks are complete bipartite graphs.\nLabeled bi-block graphs and bridgeless bi-block graphs are enumerated exactly and asymptotically\nby the number of vertices. It is proved that almost all labeled connected bi-block graphs have no\nbridges. In addition, planar bi-block graphs are enumerated, and an asymptotic estimate is found\nfor the number of such graphs.\n</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"17 4","pages":"901 - 907"},"PeriodicalIF":0.5800,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied and Industrial Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1134/S1990478923040178","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}
引用次数: 0
Abstract
A bi-block graph is a connected graph in which all blocks are complete bipartite graphs.
Labeled bi-block graphs and bridgeless bi-block graphs are enumerated exactly and asymptotically
by the number of vertices. It is proved that almost all labeled connected bi-block graphs have no
bridges. In addition, planar bi-block graphs are enumerated, and an asymptotic estimate is found
for the number of such graphs.
期刊介绍：
Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.
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