Graphs whose all maximal induced forests are of the same order

TL;DR

This paper introduces the concept of well-f-covered graphs, characterizes those with maximum induced forests of boundary order, and explores methods to construct large such graphs, enriching the understanding of graph structures.

Contribution

It defines and characterizes well-f-covered graphs, a new class where all maximal induced forests have the same order, and provides construction techniques and classifications.

Findings

Characterization of all well-f-covered graphs.

Identification of classes with boundary order maximum induced forests.

Methods for constructing large well-f-covered graphs.

Abstract

In this paper, a new concept in graphs namely well-f-coveredness is introduced. We characterize all graphs with such property, whose maximum induced forests are of boundary order. Also we prove several propositions concerning with obtaining large well-f-covered graphs from smaller ones. By the way, some interesting classes of well-f-covered graphs are characterized.