1,564 research outputs found
New measures of graph irregularity
In this paper, we define and compare four new measures of graph irregularity.
We use these measures to prove upper bounds for the chromatic number and the
Colin de Verdiere parameter. We also strengthen the concise Turan theorem for
irregular graphs and investigate to what extent Turan's theorem can be
similarly strengthened for generalized r-partite graphs. We conclude by
relating these new measures to the Randic index and using the measures to
devise new normalised indices of network heterogeneity
Uniform generation in trace monoids
We consider the problem of random uniform generation of traces (the elements
of a free partially commutative monoid) in light of the uniform measure on the
boundary at infinity of the associated monoid. We obtain a product
decomposition of the uniform measure at infinity if the trace monoid has
several irreducible components-a case where other notions such as Parry
measures, are not defined. Random generation algorithms are then examined.Comment: Full version of the paper in MFCS 2015 with the same titl
Extremal problems for the p-spectral radius of graphs
The -spectral radius of a graph of order is defined for any real
number as
The most remarkable feature of is that it
seamlessly joins several other graph parameters, e.g., is the Lagrangian, is the spectral
radius and is the number of edges. This
paper presents solutions to some extremal problems about , which are common generalizations of corresponding edge and
spectral extremal problems.
Let be the -partite Tur\'{a}n graph of order
Two of the main results in the paper are:
(I) Let and If is a -free graph of order
then unless
(II) Let and If is a graph of order with then has an edge contained in at least
cliques of order where is a positive number depending
only on and Comment: 21 pages. Some minor corrections in v
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