New results on imbalance graphic graphs

Opuscula Mathematica

article

Sergiy Kozerenko (corresponding author)¹  Andrii Serdiuk¹ 

[1]National University of Kyiv-Mohyla Academy, Faculty of Computer Sciences, Department of Mathematics

关键词: edge imbalance;    irregularity of a graph;    imbalance sequence;    graphic sequence.;   

DOI  :  10.7494/OpMath.2023.43.1.81

学科分类：环境科学（综合）

来源: AGH University of Science and Technology Press

【 摘 要 】

An edge imbalance provides a local measure of how irregular a given graph is. In this paper, we study graphs with graphic imbalance sequences. We give a new proof of imbalance graphicness for trees and use the new idea to prove that the same holds for unicyclic graphs. We then show that antiregular graphs are imbalance graphic and consider the join operation on graphs as well as the double graph operation. Our main results are concerning imbalance graphicness of three classes of block graphs: block graphs having all cut vertices in a single block; block graphs in which the subgraph induced by the cut vertices is either a star or a path. In the end, we discuss open questions and conjectures regarding imbalance graphic graphs.

【 授权许可】

CC BY-NC