dc.contributor.advisor Chandran, Sunil dc.contributor.author Bharadwaj, Subramanya B V dc.date.accessioned 2010-08-26T08:08:31Z dc.date.accessioned 2018-07-31T04:39:56Z dc.date.available 2010-08-26T08:08:31Z dc.date.available 2018-07-31T04:39:56Z dc.date.issued 2010-08-26 dc.date.submitted 2008-09 dc.identifier.uri http://etd.iisc.ac.in/handle/2005/844 dc.description.abstract In this thesis we study the isoperimetric problem on trees and graphs with bounded treewidth. Let G = (V,E) be a finite, simple and undirected graph. For let δ(S,G)= {(u,v) ε E : u ε S and v ε V – S }be the edge boundary of S. Given an integer i, 1 ≤ i ≤ | V| , let the edge isoperimetric value of G at I be defined as be(i,G)= mins v;|s|= i | δ(S,G)|. For S V, let φ(S,G) = {u ε V – S : ,such that be the vertex boundary of S. Given an integer i, 1 ≤ i ≤ | V| , let the vertex isoperimetric value of G at I be defined as bv(i,G)= The edge isoperimetric peak of G is defined as be(G) =. Similarly the vertex isoperimetric peak of G is defined as bv(G)= .The problem of determining a lower bound for the vertex isoperimetric peak in complete k-ary trees of depth d,Tdkwas recently considered in. In the first part of this thesis we provide lower bounds for the edge and vertex isoperimetric peaks in complete k-ary trees which improve those in. Our results are then generalized to arbitrary (rooted)trees. Let i be an integer where . For each i define the connected edge isoperimetric value and the connected vertex isoperimetric value of G at i as follows: is connected and is connected A meta-Fibonacci sequence is given by the reccurence a(n)= a(x1(n)+ a1′(n-1))+ a(x2(n)+ a2′(n -2)), where xi: Z+ → Z+ , i =1,2, is a linear function of n and ai′(j)= a(j) or ai′(j)= -a(j), for i=1,2. Sequences belonging to this class have been well studied but in general their properties remain intriguing. In the second part of the thesis we show an interesting connection between the problem of determining and certain meta-Fibonacci sequences. In the third part of the thesis we study the problem of determining be and bv algorithmically for certain special classes of graphs. Definition 0.1. A tree decomposition of a graph G = (V,E) is a pair where I is an index set, is a collection of subsets of V and T is a tree whose node set is I such that the following conditions are satisfied: (For mathematical equations pl see the pdf file) en_US dc.language.iso en_US en_US dc.relation.ispartofseries G22614 en_US dc.subject Computer Graphics - Algorithms en_US dc.subject Computer Graphics - Mathematical Models en_US dc.subject Isoperimetric Inequalities en_US dc.subject Meta-Fibonacci Sequences en_US dc.subject Graph Theory en_US dc.subject Trees (Graph Theory) en_US dc.subject Treewidth Graphs en_US dc.subject Weighted Graphs en_US dc.subject Infinite Binary Tree en_US dc.subject Isoperimetric Problem en_US dc.subject.classification Computer Science en_US dc.title The Isoperimetric Problem On Trees And Bounded Tree Width Graphs en_US dc.type Thesis en_US dc.degree.name MSc Engg en_US dc.degree.level Masters en_US dc.degree.discipline Faculty of Engineering en_US
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