Computing eigenvalues of distance-regular graphs and their multiplicities /
Martinez,Myla Fei Q.
Computing eigenvalues of distance-regular graphs and their multiplicities / Myla Fei Q. Martinez - 2019
Thesis ( Master of Science in Mathematics) - Mariano Marcos State University,2019.
Bibliography: leaves 60-61.
ABSTRACT MARTINEZ, MYLA FEI QUIBUYEN. Mariano State University. May 2019. COMPUTING OF DISTANCE- REGULAR GRAPHS AND THEIR MULTIPLICITIES . Major Adviser: Michelle D. Reynera. The study gave an exposition of the Section 2.5 of the paper by Edwin R. Van Dam,Jack H. Koolen and Hajime Tanaka, titled Distance-Regular Graphs , which was published in Electronic Journal of Combinatorics on April 15,2016. The study focused on the computation of eigenvalues of distance-regular graphs. Specifically, it aimed to: a) expose an alternative method in computing the eigenvalues of distance-regular graphs using intersection numbers; b) provide details on the proof of Biggs’ formula which is used in determining the multiplicities of eigenvalues; c) determine the spectra of distance-regular graphs using Biggs formula ; and d) investigate some known properties of distance-regular graphs as related to their spectra. The results of the study show that the use of the intersection matrix of a distance-regular graph and the Biggs formula provide a convenient way in determining the eigenvalues of a distance-regular graph.
Computing eigenvalues of distance-regular graphs and their multiplicities / Myla Fei Q. Martinez - 2019
Thesis ( Master of Science in Mathematics) - Mariano Marcos State University,2019.
Bibliography: leaves 60-61.
ABSTRACT MARTINEZ, MYLA FEI QUIBUYEN. Mariano State University. May 2019. COMPUTING OF DISTANCE- REGULAR GRAPHS AND THEIR MULTIPLICITIES . Major Adviser: Michelle D. Reynera. The study gave an exposition of the Section 2.5 of the paper by Edwin R. Van Dam,Jack H. Koolen and Hajime Tanaka, titled Distance-Regular Graphs , which was published in Electronic Journal of Combinatorics on April 15,2016. The study focused on the computation of eigenvalues of distance-regular graphs. Specifically, it aimed to: a) expose an alternative method in computing the eigenvalues of distance-regular graphs using intersection numbers; b) provide details on the proof of Biggs’ formula which is used in determining the multiplicities of eigenvalues; c) determine the spectra of distance-regular graphs using Biggs formula ; and d) investigate some known properties of distance-regular graphs as related to their spectra. The results of the study show that the use of the intersection matrix of a distance-regular graph and the Biggs formula provide a convenient way in determining the eigenvalues of a distance-regular graph.