Orderenergetic, hypoenergetic and equienergetic graphs resulting from some graph operations

TL;DR

This paper introduces new families of graphs characterized by their energy relative to their order, including orderenergetic, hypoenergetic, equienergetic, and related classes, through various graph operations.

Contribution

It constructs new families of graphs with specific energetic properties, expanding the understanding of graph energy classifications.

Findings

New families of orderenergetic graphs constructed

Identification of hypoenergetic graphs with specific properties

Development of methods to generate equienergetic and related graphs

Abstract

A graph G is said to be orderenergetic, if its energy equal to its order and it is said to be hypoenergetic if its energy less than its order. Two non-isomorphic graphs of same order are said to be equienergetic if their energies are equal. In this paper, we construct some new families of orderenergetic graphs, hypoenergetic graphs, equienergetic graphs, equiorderenergetic graphs and equihypoenergetic graphs.