Results 1 
5 of
5
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 ..."
Abstract

Cited by 18 (6 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 4 (3 self)
 Add to MetaCart
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.
ON UNICYCLIC REFLEXIVE GRAPHS
"... A simple graph is said to be reflexive if the second largest eigenvalue of its (0,1)adjacency matrix does not exceed 2. Based on some recent results on reflexive graphs with more cycles and some new observations, we construct in this paper several classes of maximal unicyclic reflexive graphs. 1. ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
A simple graph is said to be reflexive if the second largest eigenvalue of its (0,1)adjacency matrix does not exceed 2. Based on some recent results on reflexive graphs with more cycles and some new observations, we construct in this paper several classes of maximal unicyclic reflexive graphs. 1.
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. ..."
Abstract
 Add to MetaCart
We survey computers systems which help to obtain and sometimes provide automatically conjectures and refutations in algebraic graph theory.
DOI:10.2298/FIL0903257K UNICYCLIC REFLEXIVE GRAPHS WITH SEVEN LOADED VERTICES OF THE CYCLE ∗
"... A simple graph is reflexive if the second largest eigenvalue of its (0, 1)−adjacency matrix does not exceed 2. A vertex of the cycle of unicyclic simple graph is said to be loaded if its degree is greater than 2. In this paper we establish that the length of the cycle of unicyclic reflexive graph wi ..."
Abstract
 Add to MetaCart
A simple graph is reflexive if the second largest eigenvalue of its (0, 1)−adjacency matrix does not exceed 2. A vertex of the cycle of unicyclic simple graph is said to be loaded if its degree is greater than 2. In this paper we establish that the length of the cycle of unicyclic reflexive graph with seven loaded vertices is at most 10 and find all such graphs with the length of the cycle 10, 9 and 8. 1