Date of Publication

2024

Document Type

Master's Thesis

Degree Name

Master of Science in Mathematics

Subject Categories

Mathematics

College

College of Science

Department/Unit

Mathematics and Statistics Department

Thesis Advisor

Francis Joseph H. Campeña

Defense Panel Chair

Severino V. Gervacio

Defense Panel Member

Isagani B. Jos
Neil M. Mame

Abstract/Summary

The energy and d-energy of a graph is the sum of the absolute value of eigenvalues of the graph’s adjacency matrix and distance matrix respectively. In 2017, S. Vaidya and K. Popat determined the energy of a shadow graph of a connected graph. In this study, we determine the eigenvalues and d-eigenvalues of a closed shadow graph and closed m-shadow graph. Using those spectrum and distance spectrum that we obtained, we computed the energy and distance energy of closed shadow graph and closed m-shadow graph. We also introduce a new graph operation called anti-shadow of a graph and determine the spectrum of the graph obtained from the graph operator.

Abstract Format

html

Language

English

Format

Electronic

Keywords

Force and energy; Graph theory; Mathematical analysis

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Embargo Period

4-16-2024

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