The maximum degree of a minimally hamiltonian-connected graph
Xingzhi Zhan
TL;DR
This paper investigates the maximum degree possible in minimally hamiltonian-connected graphs of a given size, answering a question from 2016 and proposing new open problems.
Contribution
It determines the maximum degrees of such graphs for any order, providing new insights into their structural properties.
Findings
Identified maximum degrees for minimally hamiltonian-connected graphs
Answered a previously open question from 2016
Proposed two new open problems in the field
Abstract
We determine the possible maximum degrees of a minimally hamiltonian-connected graph with a given order. This answers a question posed by Modalleliyan and Omoomi in 2016. We also pose two unsolved problems.
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph theory and applications · Graph Labeling and Dimension Problems