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▫$\ell$▫-distance-balanced graphsMiklavič, Štefko ; Šparl, PrimožGraf ▫$\Gamma$▫ je razdaljno uravnotežen, če v njem za poljuben par sosednjih vozlišč ▫$u$▫ in ▫$v$▫ velja, da je število vozlišč grafa ▫$\Gamma$▫, ki so bližje ▫$u$▫ kot ▫$v$▫, enako številu vozlišč ... grafa ▫$\Gamma$▫, ki so bližje ▫$v$▫ kot ▫$u$▫. Ti grafi so sicer zanimivi že sami po sebi, v okviru teorije grafov, pomembni pa so tudi zaradi možnosti uporabe na drugih področjih, kot sta na primer matematična kemija in teorija komunikacijskih omrežij. V članku se posvetimo naravni posplošitvi koncepta razdaljne uravnoteženosti, ki jo le leta 2014 vpeljal Boštjan Frelih. Pravimo, da je graf ▫$\Gamma$▫ ▫$\ell$▫-razdaljno uravnotežen, če za poljuben par vozlišč ▫$u$▫ in ▫$v$▫ na razdalji ▫$\ell$▫ v grafu ▫$\Gamma$▫ velja, da je število vozlišč grafa ▫$\Gamma$▫, ki so bližje ▫$u$▫ kot ▫$v$▫, enako številu vozlišč grafa ▫$\Gamma$▫, ki so bližje ▫$v$▫ kot ▫$u$▫. V članku pokažemo nekaj splošnih lastnosti takšnih grafov in konstruiramo vrsto različnih primerov. Posebej se posvetimo grafom premera največ 3 in študiramo lastnost ▫$\ell$▫-razdaljne uravnoteženosti v kubičnih grafih. Med drugim se posvetimo tej lastnosti v dobro znanih posplošenih Petersenovih grafih.Source: Discrete applied mathematics. - ISSN 0166-218X (Vol. 244, July 2018, str. 143-154)Type of material - article, component part ; adult, seriousPublish date - 2018Language - englishCOBISS.SI-ID - 1540239812
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Miklavič, Štefko | 21656 |
Šparl, Primož | 23341 |
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