Degree-Based Topological Indices of Modified Petersen Graph

Abstract

Objectives:The Petersen graph is non-planar, meaning it cannot be drawn on a plane without edge crossings. This limits its use in applications requiring planar graphs, such as circuit board design, geographic mapping, or any domain where planar embeddings are essential. The Petersen graph is fixed with only 10 vertices and 15 edges. Its small size can make it unsuitable for modelling or analysing larger, more complex systems. The weakness of unsuitable for modelling or analysing larger, more complex systems estimation is the lack of consideration of the graph and it is not a function of the overall graph, because it uses the 10 vertices and 15 edges value.

Methods:It is used as a counterexample in problems involving Hamiltonian graphs.It is highly symmetric, with 120 automorphisms. Algorithms like Dijkstra’s or Floyd-Warshall can be applied to find shortest paths in the modified Petersen graph for weighted or unweighted cases.

Findings:This paper proposes a new modified Petersen Graph which means increase the vertices upto n^th term and edges are m^thterm (say k). The accuracy of the proposed method has been studied through entire paper.

Novelty:The Petersen graph is a remarkable and widely studied object in graph theory.

Vertex-transitivity: All vertices are structurally identical, meaning the graph looks the same from any vertex. Edge-transitivity: All edges are structurally identical.           Automorphism group: The graph has 120 automorphisms, equivalent to the symmetric group S_5.