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Variable Neighborhood Search for Extremal Graphs 6. Analyzing Bounds for the Connectivity Index
, 2000
"... Recently, Araujo and De la Pe~na [1] gave bounds for the connectivity index of chemical trees as a function of this index for general trees and the ramification index of trees. They also gave bounds for the connectivity index of chemical graphs as a function of this index for maximal subgraphs which ..."
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Cited by 17 (5 self)
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Recently, Araujo and De la Pe~na [1] gave bounds for the connectivity index of chemical trees as a function of this index for general trees and the ramification index of trees. They also gave bounds for the connectivity index of chemical graphs as a function of this index for maximal subgraphs which are trees and the cyclomatic number of the graphs. The ramification index of a tree is first shown to be equal to the number of pending vertices minus 2. Then, in view of extremal graphs obtained with the system AutoGraphiX, all bounds of Araujo and De la Pe\~na [1] are improved, yielding tight bounds, and in one case corrected. Moreover, chemical trees of given order and number of pending vertices with minimum and with maximum connectivity index are characterized.
A DATABASE OF STAR COMPLEMENTS OF GRAPHS
 UNIV. BEOGRAD. PUBL. ELEKTROTEHN. FAK. SER. MAT. 9 �1998�, 103�112.
, 1998
"... Let µ be an eigenvalue of the graph G with multiplicity k. A star complement for µ in G is an induced subgraph H = G  X such that X = k and µ is not an eigenvalue of G  X. The database contains about 1500 triples (G, H, µ) and is available as a supplement to the programming package "Graph". It w ..."
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Cited by 4 (3 self)
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Let µ be an eigenvalue of the graph G with multiplicity k. A star complement for µ in G is an induced subgraph H = G  X such that X = k and µ is not an eigenvalue of G  X. The database contains about 1500 triples (G, H, µ) and is available as a supplement to the programming package "Graph". It was produced using (a) "Graph" itself, (b) programs developed independently by M. Lepovic, and (c) data from other sources cited in the bibliography. This paper contains a description of the database and a commentary which explains how some interesting graphs can be obtained by extending appropriate star complements.
Computers and Discovery in Algebraic Graph Theory
 Edinburgh, 2001), Linear Algebra Appl
, 2001
"... We survey computers systems which help to obtain and sometimes provide automatically conjectures and refutations in algebraic graph theory. ..."
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Cited by 1 (0 self)
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We survey computers systems which help to obtain and sometimes provide automatically conjectures and refutations in algebraic graph theory.