Title

On the vector space of a-like matrices for tadpole graphs

Date of Publication

2016

Document Type

Bachelor's Thesis

Degree Name

Bachelor of Science in Mathematics with specialization in Business Applications

Subject Categories

Mathematics

College

College of Science

Department/Unit

Mathematics and Statistics Department

Thesis Adviser

Francis Joseph H. Campena

Abstract/Summary

Consider a simple undirected graph {u100000} with vertex set X. Let MatX(R) denote the R-algebra of matrices with entries in R and with the rows and columns indexed by X. Let A 2 MatX(R) denote an adjacency matrix of {u100000}. For B 2 MatX(R), B is de ned to be A-like whenever the following conditions are satis ed: (i) BA = AB and (ii) for all x y 2 X that are not equal or adjacent, the (x y)-entry of B is zero. Let L denote the subspace of MatX(R) consisting of the A-like elements. The subspace L is decomposed into the direct sum of its symmetric part, and antisymmetric part. This study shows that if {u100000} is T3 n, a tadpole graph with a cycle of order 3 and a path of order n, where n 1, then a basis for L is fI A !g, where A is an adjacency matrix of {u100000}, I is the identity matrix of size jXj, and ! is a block matrix as shown below: In+1 N NT E where N is an (n + 1) 2 zero matrix and E is matrix 0 1 1 0 : If {u100000} is Tm n, where m 4, and n 1, a basis for L is fA Ig.

Abstract Format

html

Language

English

Format

Electronic

Accession Number

CDTU021038

Shelf Location

Archives, The Learning Commons, 12F, Henry Sy Sr. Hall

Physical Description

1 computer disc ; 4 3/4 in.

Keywords

Matrices; Graph algorithms; Graph theory; Computer algorithms

Embargo Period

5-11-2021

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