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dc.contributor.adviserDiesto, Severino D.
dc.contributor.authorVencer, Norma Luz C.
dc.date.accessioned2021-10-04T03:07:11Z
dc.date.available2021-10-04T03:07:11Z
dc.date.issued2006
dc.identifier.citationVencer, N. L. C. (2006). On applications of the retracing method for distance-regular graph (Unpublished Master’s thesis). De La Salle University, Manila.en_US
dc.identifier.urihttps://hdl.handle.net/20.500.12852/1472
dc.descriptionAbstract onlyen_US
dc.description.abstractThis thesis is an exposition of the article written by Akira Hiraki entitled Applications of Retracing Method for Distance-Regular Graphs published in European Journal of Combinatorics, April 2004. The main results of the article are as follows: \(\mathbf{Theorem \,1.1} \, \mathrm{Let}\, \Gamma \,\mathrm{be\,a\,distance-regular\,graph \,of \,diameter} \,d \,\mathrm{with}\) \[r = |\{ i|(c_{i}, a_{i}, b_{i}) = (c_{1}, a_{1}, b_{1})\}| \geq 2\] \(\mathrm{and} \, c_{r+1} \geq 2. \, \mathrm{Let} \, m, s \, \mathrm{and} \, t \, \mathrm{be\,positive\,integers\,with\,} s \leq \, m, m + t \leq d \, \mathrm{and} \, (s, t)\) \( \neq (1,1). \mathrm{Suppose} \, b_{m-s+1} = \cdots = b_{m} = 1 + b_{m+1}, c_{m+1} = \cdots = c_{m+t} = 1 + c_{m}\) \(\mathrm{and} \, a_{m-s+2} = \cdots = a_{m+t-1} = 0. \, \mathrm{Then\,the\,following\,hold.}\) \[\mathrm{If}\,b_{m+1} ≥ 2,\,\mathrm{then} \,t ≤ r – 2 \lfloor\,s/3\,\rfloor. \tag{1}\] \[\mathrm{If} \,c_{m} ≥ 2, \mathrm{then} \,s ≤ r – 2 \lfloor\,t/3\,\rfloor. \tag{2}\] \(\mathbf{Corollary \,1.2} \, \mathrm{Under\,the\,assumption\,of\,Theorem\,1.1,\,the\,following\,hold.}\) \[\mathrm{If} \, r = t \, \mathrm{and} \, b_{m+1} \geq 2, \, \mathrm{then} \, s \leq 2. \tag{1}\] \[\mathrm{If} \, r = s \, \mathrm{and} \, c_{m} \geq 2, \, \mathrm{then} \, t \leq 2. \tag{2}\] \(\mathbf{Corollary \,1.3.} \, \mathrm{Let} \, \Gamma \, \mathrm{be\,a\,distance-regular\,graph\,of\,valency} \, k \geq \, 3 \, \mathrm{with}\) \( c_{1} = \cdots = c_{r} = 1, c_{r+1} = \cdots = c_{r+t} = 2 \, \mathrm{and} \, a_{1} = \cdots = a_{r+t-1} = 0.\) \[\mathrm{If} \, k \geq 4, \, \mathrm{then} \, t \leq r-2 \lfloor\,r/3\rfloor. \tag{1}\] \[\mathrm{If} \, 2 \leq t = r, \, \mathrm{then} \, \Gamma \, \mathrm{is \, either \, the \, Odd \, graph, \, or \, the \, doubled \, Odd \, graph.}\tag{2}\] \[\mathrm{If} \, 2 \leq t = r – 1, \, \mathrm{then} \, \Gamma \, \mathrm{is \, the \, Foster \, graph.} \tag{3}\]en_US
dc.description.sponsorshipAssociations of Christian Universities and Colleges in Asiaen_US
dc.format.extentvi, 76 leavesen_US
dc.language.isoenen_US
dc.subject.ddcGSL Theses 510.72 V552en_US
dc.subject.lcshGraphic methodsen
dc.titleOn applications of the retracing method for distance-regular graphen_US
dc.typeThesisen_US
dc.description.bibliographicalreferencesIncludes bibliographical referencesen_US
dc.contributor.chairPascasio, Arlene A.
dc.contributor.committeememberGervacio, Severino V.
dc.contributor.committeememberFortes, Erminda C.
dc.contributor.departmentMathematics Department, College of Scienceen_US
dc.description.degreeMaster of Science in Mathematicsen_US


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