<?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>S1409-24332016000200409</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[A combinatorial problem on a directed graph]]></article-title>
<article-title xml:lang="es"><![CDATA[Un problema combinatorio basado en un grafo orientado]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Marrero]]></surname>
<given-names><![CDATA[Osvaldo]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Pasles]]></surname>
<given-names><![CDATA[PaulC.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Villanova University  ]]></institution>
<addr-line><![CDATA[Villanova Pennsylvania]]></addr-line>
<country>US</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Villanova University  ]]></institution>
<addr-line><![CDATA[Villanova Pennsylvania]]></addr-line>
<country>US</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2016</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2016</year>
</pub-date>
<volume>23</volume>
<numero>2</numero>
<fpage>409</fpage>
<lpage>420</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_arttext&amp;pid=S1409-24332016000200409&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_abstract&amp;pid=S1409-24332016000200409&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.sa.cr/scielo.php?script=sci_pdf&amp;pid=S1409-24332016000200409&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[AbstractWe consider two options for a particle's entire journey through a certain directed graph. Both options involve a random assignment to the journey route to be followed. We are interested in the option that offers, on average, the shortest route. Therefore, we determine the average journey length for each of the two options. As part of our analysis, we prove some combinatorial identities that appear to be new. Some suggestions for further work are given.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[ResumenSe consideran dos opciones para la jornada total de una partícula que se desplaza a través de un cierto grafo orientado. Bajo ambas opciones, la ruta de la jornada es asignada aleatoriamente. Nos interesa saber la opción bajo la cual uno espera la ruta más corta. Por eso, para cada opción, determinamos la esperanza matemática del largo de la ruta. Al parecer novedosas, algunas identidades combinatorias son demostradas como parte de nuestro análisis. Para concluir, mencionamos varias oportunidades para futuros estudios.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[directed graphs]]></kwd>
<kwd lng="en"><![CDATA[games on graphs]]></kwd>
<kwd lng="en"><![CDATA[combinatorial identities]]></kwd>
<kwd lng="en"><![CDATA[combinatorial probability]]></kwd>
<kwd lng="es"><![CDATA[grafos orientados]]></kwd>
<kwd lng="es"><![CDATA[juegos en grafos]]></kwd>
<kwd lng="es"><![CDATA[identidades combinatorias]]></kwd>
<kwd lng="es"><![CDATA[probabilidad combinatoria]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Chartrand]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<name>
<surname><![CDATA[Lesniak]]></surname>
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<surname><![CDATA[Zhang]]></surname>
<given-names><![CDATA[P.]]></given-names>
</name>
</person-group>
<source><![CDATA[Graphs &amp; Digraphs]]></source>
<year>2010</year>
<edition>5th</edition>
<publisher-loc><![CDATA[Boca Raton FL ]]></publisher-loc>
<publisher-name><![CDATA[CRC Press]]></publisher-name>
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<person-group person-group-type="author">
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</name>
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<surname><![CDATA[Welsh]]></surname>
<given-names><![CDATA[D.]]></given-names>
</name>
</person-group>
<source><![CDATA[Probability: An Introduction]]></source>
<year>2014</year>
<edition>2d</edition>
<publisher-loc><![CDATA[Oxford, United Kingdom ]]></publisher-loc>
<publisher-name><![CDATA[Oxford University Press]]></publisher-name>
</nlm-citation>
</ref>
</ref-list>
</back>
</article>
