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51 
Minimal congestion treesDawson, Shelly Jean 01 January 2006 (has links)
Analyzes the results of M.I. Ostrovskii's theorem of inequalities which estimate the minimal edge congestion for finite simple graphs. Uses the generic results of the theorem to examine and further reduce the parameters of inequalities for specific families of graphs, particularly complete graphs and complete bipartite graphs. Also, explores a possible minimal congestion tree for some grids while forming a conjecture for all grids.

52 
Greatest common dwisors and least common multiples of graphsSaba, Farrokh 11 1900 (has links)
Chapter I begins with a brief history of the topic of greatest common subgraphs.
Then we provide a summaiy of the work done on some variations of greatest common
subgraphs. Finally, in this chapter we present results previously obtained on greatest
common divisors and least common multiples of graphs.
In Chapter II the concepts of prime graphs, prime divisors of graphs, and primeconnected
graphs are presented. We show the existence of prime trees of any odd size
and the existence of primeconnected trees that are not prime having any odd composite
size. Then the number of prime divisors in a graph is studied. Finally, we present
several results involving the existence of graphs whose size satisfies some prescribed
condition and which contains a specified number of prime divisors.
Chapter III presents properties of greatest common divisors and least common
multiples of graphs. Then graphs with a prescribed number of greatest common
divisors or least common multiples are studied.
In Chapter IV we study the sizes of greatest common divisors and least common
multiples of specified graphs. We find the sizes of greatest common divisors and least
common multiples of stars and that of stripes. Then the size of greatest common
divisors and least common multiples of paths and complete graphs are investigated. In
particular, the size of least common multiples of paths versus K3 or K4 are
determined. Then we present the greatest common divisor index of a graph and we
determine this parameter for several classes of graphs.
iii
In Chapter V greatest common divisors and least common multiples of digraphs
are introduced. The existence of least common mutliples of two stars is established,
and the size of a least common multiple is found for several pairs of stars. Finally, we
present the concept of greatest common divisor index of a digraph and determine it for
several classes of digraphs.
iv / Mathematical Sciences / Ph. D. (Mathematical sciences)

53 
Minimal realization of RC oneport何嘉良, Ho, Kaleung. January 1973 (has links)
published_or_final_version / Electrical Engineering / Master / Master of Philosophy

54 
Minmax theorems on feedback vertex setsLi, Yinchiu., 李燕超. January 2002 (has links)
published_or_final_version / Mathematics / Master / Master of Philosophy

55 
Cliques and independent setsHaviland, Julie Sarah January 1989 (has links)
No description available.

56 
Restricted edgecolouringsHind, Hugh Robert Faulkner January 1988 (has links)
No description available.

57 
Simplicial decompositions and universal graphsDiestal, R. January 1986 (has links)
No description available.

58 
PARTITIONING STRONGLY REGULAR GRAPHS (BALANCED INCOMPLETE BLOCK DESIGNS, ASSOCIATION SCHEMES).GOSSETT, ERIC JAMES. January 1984 (has links)
A strongly regular graph can be design partitioned if the vertices of the graph can be partitioned into two sets V and B such that V is a coclique and every vertex in B is adjacent to the same number of vertices in V. In this case, a balanced incomplete block design can be defined by taking elements of V as objects and elements of B as blocks. Many strongly regular graphs can be design partitioned. The nation of design partitioning is extended to a partitioning by a generalization of block designs called orderfree designs. All strongly regular graphs can be partitioned via orderfree designs. Orderfree designs are used to show the nonexistence of a strongly regular graph with parameters (50,28,18,12). The existence of this graph was previously undecided. A computer algorithm that attempts to construct the adjacency matrix of a strongly regular graph (given a suitable orderfree design) is presented. Two appendices related to the algorithm are included. The first lists all parameter sets (n,a,c,d) with n ≤ 50 and a ≠ d that satisfy the standard feasibility conditions for strongly regular graphs. Additional information is included for each set. The second appendix contains adjacency matrices (with the partitioning by cocliques and orderfree designs exhibited) for most of the parameter sets in the first appendix. The theoretical development is presented in the context of association schemes. Partitioning by orderfree designs extends naturally to any association scheme when cocliques are generalized to {Ø,i} cliques. This extended partitioning is applied to generalized hexagons.

59 
On decomposition of complete infinite graphs into spanning treesKing, Andrew James Howell January 1990 (has links)
No description available.

60 
Edgecolouring and Ifactors in graphsLienart, Emmanuelle Anne Sophie January 2000 (has links)
No description available.

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