What type of study is this?

This is a Quantitative Study study.

October 9, 2025Open Access

The index of unbalanced signed complete graphs whose negative-edge-induced subgraph is K₂, ₂-minor free

Key Points

The study identifies extremal signed complete graphs maximizing the index, while exploring restrictions of K_{2,2}-minor free subgraphs.
It characterizes the second maximum index scenarios, focusing on structures devoid of certain minors for enhanced analysis.
The concepts of minor free graphs and their implications on signed graphs offer insights into possible extremum problems and solutions.
Understanding the index in these contexts paves the way for further exploration in graph theory related to minors and their properties.

Abstract

Let = (Kₙ, H^-) be a signed complete graph with the negative edges induced subgraph H. According to the properties of the negative-edge-induced subgraph, characterizing the extremum problem of the index of the signed complete graph is a concern in signed graphs. A graph G is called H-minor free if G has no minor which is isomorphic to H. In this paper, we characterize the extremal signed complete graphs that achieve the maximum and the second maximum index when H is a K₂, ₂-minor free spanning subgraph of Kₙ.

Read Full Paperexternally

Bookmark

View Full Paper

Cite This Study

Qin et al. (Wed,) studied this question.

synapsesocial.com/papers/68e82b12e7fc21a30050037f https://doi.org/https://doi.org/10.48550/arxiv.2505.09136