Results 11  20
of
70
G.: An iterative restart variable neighbourhood search for the examination timetabling problem
 Practice and Theory of Automated Timetabling. LNCS
, 1996
"... Producing good quality examination timetables is a difficult task which is faced by many academic institutions. Due to the complexity and the large size of the realworld university examination timetabling problems, it is difficult to obtain an optimal solution. Indeed, due to the complex nature of ..."
Abstract

Cited by 4 (4 self)
 Add to MetaCart
Producing good quality examination timetables is a difficult task which is faced by many academic institutions. Due to the complexity and the large size of the realworld university examination timetabling problems, it is difficult to obtain an optimal solution. Indeed, due to the complex nature of the problem, it is questionable if an end user would recognise a truly optimal solution.
THE MINIMUM SPECTRAL RADIUS OF GRAPHS WITH A GIVEN CLIQUE NUMBER
, 2008
"... In this paper, it is shown that among connected graphs with maximum clique size ω, the minimum value of the spectral radius of adjacency matrix is attained for a kite graph P Kn−ω,ω, which consists of a complete graph Kω to a vertex of which a path Pn−ω is attached. For any fixed ω, a small interv ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
(Show Context)
In this paper, it is shown that among connected graphs with maximum clique size ω, the minimum value of the spectral radius of adjacency matrix is attained for a kite graph P Kn−ω,ω, which consists of a complete graph Kω to a vertex of which a path Pn−ω is attached. For any fixed ω, a small interval to which the spectral radii of kites P Km,ω, m ≥ 1, belong is exhibited.
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

Cited by 4 (0 self)
 Add to MetaCart
We survey computers systems which help to obtain and sometimes provide automatically conjectures and refutations in algebraic graph theory.
inequalities among graph invariants: using GraPHedron to uncover optimal relationships. Accepted for publication in Networks (2008
"... Optimality of a linear inequality in finitely many graph invariants is defined through a geometric approach. For a fixed number of graph nodes, consider all the tuples of values taken by the invariants on a selected class of graphs. Then form the polytope which is the convex hull of all these tupl ..."
Abstract

Cited by 4 (3 self)
 Add to MetaCart
(Show Context)
Optimality of a linear inequality in finitely many graph invariants is defined through a geometric approach. For a fixed number of graph nodes, consider all the tuples of values taken by the invariants on a selected class of graphs. Then form the polytope which is the convex hull of all these tuples. By definition, the optimal linear inequalities correspond to the facets of this polytope. They are finite in number, are logically independent, and generate precisely all the linear inequalities valid on the class of graphs. The computer system GraPHedron, developed by some of the authors, is able to produce experimental data about such inequalities for a “small ” number of nodes. It greatly helps conjecturing optimal linear inequalities, which are then hopefully proved for any node number. Two examples are investigated here for the class of connected graphs. First, all the optimal linear inequalities in the stability number and the link number are obtained. To this aim, a problem of Ore (1962) related to Turán Theorem (1941) is solved. Second, several optimal inequalities are established for three invariants: the maximum degree, the irregularity, and the diameter.
Solutions to two unsolved questions on the best upper bound for the Randić index R−1 of trees
 MATCH Commun. Math. Comput. Chem
"... The general Randic index R(G) of a graph G is dened as the sum of the weights (d(u)d(v)) of all edges uv of G, where d(u) denotes the degree of a vertex u in G and is an arbitrary real number. Clark and Moon gave the lower and upper bounds for the Randic index R1 of trees with order n. The lower b ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
The general Randic index R(G) of a graph G is dened as the sum of the weights (d(u)d(v)) of all edges uv of G, where d(u) denotes the degree of a vertex u in G and is an arbitrary real number. Clark and Moon gave the lower and upper bounds for the Randic index R1 of trees with order n. The lower bound is sharp. However, a sharp upper bound has not been obtained for a long time. Clark and Moon proposed two unsolved questions on the upper bound. In this paper, we give positive answers to the two questions. We show that limn!1f(n)=n = 15=56, and give a sharp upper bound for which there are innitely many trees of order n whose values of Randic index R1 attain the bound. Supported by National Science Foundation of China. 1
A Survey of Research on Automated Mathematical ConjectureMaking
 FAJTLOWICZ (EDITORS), AMERICAN MATHEMATICAL SOCIETY
, 2005
"... The first attempt at automating mathematical conjecturemaking appeared in the late1950s. It was not until the mid1980s though that a program produced statements of interest to research mathematicians and actually contributed to the advancement of mathematics. A central and important idea underlyi ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
(Show Context)
The first attempt at automating mathematical conjecturemaking appeared in the late1950s. It was not until the mid1980s though that a program produced statements of interest to research mathematicians and actually contributed to the advancement of mathematics. A central and important idea underlying this program is the Principle of the Strongest Conjecture: make the strongest conjecture for which no counterexample is known. These two programs as well as other attempts to automate mathematical conjecturemaking are surveyed—the success of a conjecturemaking program, it is found, correlates strongly whether the program is designed to produce statements that are relevant to answering or advancing our mathematical questions.
On the Randic ́ index of cacti
"... The Randic ́ index of an organic molecule whose molecular graph is G is the sum of the weights (d(u)d(v))− 1 2 of all edges uv of G, where d(u) and d(v) are the degrees of the vertices u and v in G. In the paper, we give a sharp lower bound on the Randić index of cacti. ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
The Randic ́ index of an organic molecule whose molecular graph is G is the sum of the weights (d(u)d(v))− 1 2 of all edges uv of G, where d(u) and d(v) are the degrees of the vertices u and v in G. In the paper, we give a sharp lower bound on the Randić index of cacti.
ON THE ZAGREB INDEX INEQUALITY OF GRAPHS WITH PRESCRIBED VERTEX DEGREES
, 2010
"... On the Zagreb index inequality of graphs with prescribed vertex degrees ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
(Show Context)
On the Zagreb index inequality of graphs with prescribed vertex degrees
On the spectral radius of graphs with a given domination number
 Linear Algebra Appl
"... ..."
(Show Context)