<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>1409-2433</journal-id>
<journal-title><![CDATA[Revista de Matemática Teoría y Aplicaciones]]></journal-title>
<abbrev-journal-title><![CDATA[Rev. Mat]]></abbrev-journal-title>
<issn>1409-2433</issn>
<publisher>
<publisher-name><![CDATA[Centro de Investigaciones en Matemática Pura y Aplicada (CIMPA) y Escuela de Matemática, San José, Costa Rica.]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1409-24332015000200293</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Graph irregularity: discussion, graph extensions and new proposals]]></article-title>
<article-title xml:lang="es"><![CDATA[Irregularidad de grafos: discusión, extensiones de grafos y nuevas propuestas]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Boaventura-Netto]]></surname>
<given-names><![CDATA[Paulo Oswaldo]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Federal University of Rio de Janeiro  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>BR</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2015</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2015</year>
</pub-date>
<volume>22</volume>
<numero>2</numero>
<fpage>293</fpage>
<lpage>310</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_arttext&amp;pid=S1409-24332015000200293&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_abstract&amp;pid=S1409-24332015000200293&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_pdf&amp;pid=S1409-24332015000200293&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[AbstractThis paper presents some measures of graph irregularity found in the literature. From their discussion two important points appear: first, the absence of relationship between all of them, but a single exception, with the structures of the corresponding graphs and, moreover, their known extremal values correspond to graphs having degree sequences with few different values. Two new measures are proposed, seeking to meet these points. Their values are calculated for extremal graphs associated with other measures and for antiregular graphs. Finally, we calculate the boxplots of all these measures for some sets of graphs taken from the literature and also for four sets where the ordered degree sequences are constant. All measures involved have polynomial complexity.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[ResumenEste artículo presenta un análisis de las medidas de irregularidad de grafos que se encuentran en la literatura. Desde su discusión dos puntos importantes aparecen: primero, la ausencia de relación entre todos ellos, sino una sola excepción - con las estructuras de los grafos correspondientes y, además, sus valores extremales conocidos corresponden a grafos que tienen secuencias de grados con pocos valores diferentes. Se proponen dos nuevas medidas, tratando de cumplir con estos puntos. Sus valores se calculan para grafos extremales asociados con otras medidas y para grafos antiregulares. Por último, se determinan los gráficos de quartiles o boxplots de todas estas medidas, para algunos conjuntos de grafos de la literatura y para cuatro conjuntos donde las secuencias ordenadas de grados son constantes. Todas las medidas estudiadas tienen complejidad polinómica.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Graphs]]></kwd>
<kwd lng="en"><![CDATA[irregularity]]></kwd>
<kwd lng="en"><![CDATA[irregularity measures]]></kwd>
<kwd lng="en"><![CDATA[graph extensions]]></kwd>
<kwd lng="es"><![CDATA[grafos]]></kwd>
<kwd lng="es"><![CDATA[irregularidad]]></kwd>
<kwd lng="es"><![CDATA[medidas de irregularidad]]></kwd>
<kwd lng="es"><![CDATA[extensiones de grafos]]></kwd>
</kwd-group>
</article-meta>
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