Journal article

Edge Imbalance Sequences And Their Graphicness

Year:

2019

Published in:

Journal of Advanced Mathematical Studies
edge imbalance
graphic sequence
graph products
graph irregularity

The imbalance of a given edge in a graph is the absolute difference between the degrees of its vertices. The multiset of all edge imbalances in G is called its imbalance sequence and denoted by M_{G}. In this paper, we focus on unary and binary graph operations that preserve the graphicness of imbalance sequences. For example, we prove that if a graph G' is obtained from G by "replacing" each vertex with a complete graph of sufficiently large order, then the graphicness of M_{G} implies the graphicness of M_{G'}. Also, we discuss several conjectures related to the graphicness of the imbalance sequence of a graph and explore connections between them.

Other publications by

24 publications found

2025
Journal article

On Strongly Connected Markov Graphs Of Maps On Combinatorial Trees

Publisher: Discrete Mathematics Letters

Authors: Sergiy Kozerenko

2023
Journal article

Unique Eccentric Point Graphs And Their Eccentric Digraphs

Publisher: Discrete Mathematics

Authors: Sergiy Kozerenko, Artem Hak, Vladyslav Haponenko, Andrii Serdiuk

2024
Journal article

All‑Path Convexity: Two Characterizations, General Position Number, And One Algorithm

Publisher: Discrete Mathematics Letters

Authors: Sergiy Kozerenko, Vladyslav Haponenko

2016
Journal article

Markov Graphs Of One–Dimensional Dynamical Systems And Their Discrete Analogues

Publisher: Romanian Journal of Mathematics and Computer Science

Authors: Sergiy Kozerenko

2025
Conference proceedings

Полідерева зі слабко зв’язними реберними орграфами

Publisher: КПІ ім. Ігоря Сікорського

Authors: Sergiy Kozerenko, Bohdan-Yarema Dekhtiar