Shortest Connectivity: An Introduction with Applications in PhylogenySpringer Science & Business Media, 2004. 11. 19. - 268ÆäÀÌÁö The aim in this graduate level text is to outline the key mathematical concepts that underpin these important questions in applied mathematics. These concepts involve discrete mathematics (particularly graph theory), optimization, computer science, and several ideas in biology. |
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... Vertex Mean Graphs A.Lourdusamy and Sherry George Department of Mathematics, Manonmaniam Sundaranar University St. Xavier's College (Autonomous), Palayamkottai, Tirunelveli - 627002, India lourdusamy15@gmail.com Abstract: A super vertex ...
... Vertex Mean Graphs A.Lourdusamy and Sherry George Department of Mathematics, Manonmaniam Sundaranar University St. Xavier's College (Autonomous), Palayamkottai, Tirunelveli - 627002, India lourdusamy15@gmail.com Abstract: A super vertex ...
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... vertices provided that n ¡Ã 2 and m ¡Ã 2 (see also Lemma 2.10 below). Moreover, for any n ¡Ã 2, Kn ¡ýK2 has exactly n S-vertices. Note that a graph containing a Smarandache vertex should have at least four vertices and three edges and ...
... vertices provided that n ¡Ã 2 and m ¡Ã 2 (see also Lemma 2.10 below). Moreover, for any n ¡Ã 2, Kn ¡ýK2 has exactly n S-vertices. Note that a graph containing a Smarandache vertex should have at least four vertices and three edges and ...
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TWO CLASSICAL OPTIMIZATION PROBLEMS | 1 |
12 MINIMUM SPANNING TREES | 11 |
GAUSS QUESTION | 21 |
22 EXAMPLES AND EXERCISES | 27 |
23 REFERENCES | 30 |
24 A FIRST ANALYSIS OF STEINERS PROBLEM | 31 |
25 STEINERS PROBLEM IN GRAPHS | 46 |
WHAT DOES SOLUTION MEAN? | 55 |
53 APPLICATIONS AND RELATED QUESTIONS | 160 |
AN ANALYSIS OF STEINERS PROBLEM IN PHYLOGENETIC SPACES | 171 |
62 MORE ABOUT TREES | 174 |
63 CLUSTER ANALYSIS | 192 |
64 SPANNING TREES | 199 |
65 COUNTING THE ELEMENTS IN DISCRETE METRIC SPACES | 201 |
66 FERMATS PROBLEM IN SEVERAL DISCRETE METRIC SPACES | 206 |
TREE BUILDING ALGORITHMS | 209 |
32 DOES A SOLUTION EXIST? | 58 |
33 DOES AN ALGORITHM EXIST? | 59 |
34 DOES AN EFFICIENT ALGORITHM EXIST? | 61 |
35 DOES AN APPROXIMATION EXIST? | 74 |
NETWORK DESIGN PROBLEMS | 83 |
42 Several Variants | 92 |
A NEW CHALLENGE THE PHYLOGENY | 123 |
51 PHYLOGENETIC TREES | 124 |
52 PHYLOGENETIC SPACES | 131 |
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algorithm alphabet approximation binary tree biology called classification combinatorial common ancestor compute connected graph Consequently consider construction contains convex cost measure cycle defined degree denotes discuss distance dold Euclidean plane Euclidean space Eulerian Eulerian cycle evolution exactly Fermat's Problem find an MST finite set geometry given points graph G Hence heuristic integer internal vertices k-SMT L(MST L(SMT Let G letters mathematical matrix Maximum Parsimony method metric space metric space X,p minimal length minimum spanning tree Molecular Moreover multiple alignment N-tree N©û NP-complete NP-hard number of vertices Observation pair phylogenetic space phylogenetic trees Problem Given Problem in graphs procedure protein real number scoring system set of given set of points shortest path shortest tree solution species Steiner Minimal Tree Steiner points Steiner ratio Steiner Tree Steiner's Problem subset taxa Theorem theory Torricelli point tree interconnecting Tree Problem ultrametric space unit ball v©û vertex words