Work

Trace of the Adjacency Matrix of the Star Graph and Complete Bipartite Graph Raised to a Positive Integer Power

Year: 2025

Type: article

Abstract: This research aims to derive the general form of the trace matrix of adjacency from star graphs and complete bipartite graphs with size n × n and raised to a positive integer power. To obtain the general form of the trace matrix of adjacency for these graphs, we first derive the general form of the adjacency matrix raised to a positive integer power for each given graph. The general form 14 of matrix exponentiation is proven using mathematical induction. The trace matrix of adjacency for each graph raised to a positive integer power is obtained through a direct proof based on the definition of the trace matrix. Additionally, applications of the trace matrix of adjacency from star graphs and complete bipartite graphs with size n × n and raised to a positive integer power are provided in the form of examples.

Source: CAUCHY Jurnal Matematika Murni dan Aplikasi

DOI: 10.18860/cauchy.v10i2.34255

Authors: Corry Corazon Marzuki, Fitri Aryani, Sri Basriati, Yuslenita Muda

Institution: Universitas Islam Negeri Sultan Syarif Kasim Riau

Language: English

Topic: Graph theory and applications

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $110

OpenAlex ID: W4416687937

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