2025/06/30 by Sayan Deb Dutta, Dutta, Sayan, Sohom Gupta +1
Computer Science · Mathematics · #Advanced Graph Theory Research #Limits and Structures in Graph Theory #Graph Labeling and Dimension Problems
paper · pdf · doi:10.48550/arxiv.2506.23965
A graph \mathcal G = (\mathcal V, \mathcal E) is said to satisfy the Neighbour Sum Property if there exists some f:\mathcal V→\mathbb R such that f\not≡ 0 and it maps every vertex to the sum of the values taken by its neighbours. In this article, we provide an algorithm to check whether a given finite tree satisfies the neighbour sum property. We also find a large class of trees on n vertices that satisfy the property.