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Title:
On the Vertex Energy of Small Integral Trees
Authors:
Sharathkumar Hunjanalu Thimmarayappa ORCID iD 0009-0004-2039-2862
Shrikanth Chikkenahalli Krishnamurthy ORCID iD 0009-0003-4137-5001
Narahari Narasimha Swamy ORCID iD 0000-0002-9243-840X
Hadonahally Mudalagiraiah Nagesh ORCID iD 0000-0001-9864-8937
Uppari Vijaya Chandra Kumar
Volume
95
Issue
2
Year
2026
Pages
467-485
Abstract

Introduced by Arizmendi et al. in the year 2018, the energy \( \mathcal{E}_G(v) \) of a vertex \( v \) of a graph gives the graph energy distribution over all its vertices and is found to be very useful in understanding the influence of individual vertices on the overall graph energy. In this paper, we determine the vertex energies of some particular classes of trees. Consequently, we obtain the vertex energies of all integral trees on at most 30 vertices.