Extremal Edge-Girth-Regular Graphs

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27240%2F21%3A10248248" target="_blank" >RIV/61989100:27240/21:10248248 - isvavai.cz</a>

Výsledek na webu

<a href="https://link.springer.com/article/10.1007%2Fs00373-021-02368-9" target="_blank" >https://link.springer.com/article/10.1007%2Fs00373-021-02368-9</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00373-021-02368-9" target="_blank" >10.1007/s00373-021-02368-9</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Extremal Edge-Girth-Regular Graphs

Popis výsledku v původním jazyce

An edge-girth-regular egr(v, k, g, λ)-graph Γ is a k-regular graph of order v and girth g in which every edge is contained in λ distinct g-cycles. Edge-girth-regularity is shared by several interesting classes of graphs which include edge- and arc-transitive graphs, Moore graphs, as well as many of the extremal k-regular graphs of prescribed girth or diameter. Infinitely many egr(v, k, g, λ)-graphs are known to exist for sufficiently large parameters (k, g, λ), and in line with the well-known Cage Problem we attempt to determine the smallest graphs among all edge-girth-regular graphs for given parameters (k, g, λ). To facilitate the search for egr(v, k, g, λ)-graphs of the smallest possible orders, we derive lower bounds in terms of the parameters k, g and λ. We also determine the orders of the smallest egr(v, k, g, λ)-graphs for some specific parameters (k, g, λ), and address the problem of the smallest possible orders of bipartite edge-girth-regular graphs.

Název v anglickém jazyce

Extremal Edge-Girth-Regular Graphs

Popis výsledku anglicky

An edge-girth-regular egr(v, k, g, λ)-graph Γ is a k-regular graph of order v and girth g in which every edge is contained in λ distinct g-cycles. Edge-girth-regularity is shared by several interesting classes of graphs which include edge- and arc-transitive graphs, Moore graphs, as well as many of the extremal k-regular graphs of prescribed girth or diameter. Infinitely many egr(v, k, g, λ)-graphs are known to exist for sufficiently large parameters (k, g, λ), and in line with the well-known Cage Problem we attempt to determine the smallest graphs among all edge-girth-regular graphs for given parameters (k, g, λ). To facilitate the search for egr(v, k, g, λ)-graphs of the smallest possible orders, we derive lower bounds in terms of the parameters k, g and λ. We also determine the orders of the smallest egr(v, k, g, λ)-graphs for some specific parameters (k, g, λ), and address the problem of the smallest possible orders of bipartite edge-girth-regular graphs.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2021

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Graphs and Combinatorics

ISSN

0911-0119

e-ISSN

—

Svazek periodika

37

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

JP - Japonsko

Počet stran výsledku

16

Strana od-do

2139-2154

Kód UT WoS článku

000674125900002

EID výsledku v databázi Scopus

2-s2.0-85110415056