Temat: super edge-connected - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Sufficient Conditions for Maximally Edge-Connected and Super-Edge-Connected Graphs Depending on The Clique Number
Autorzy:: Volkmann, Lutz
Powiązania:: https://bibliotekanauki.pl/articles/31343389.pdf
Data publikacji:: 2019-05-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: edge-connectivity
clique number
maximally edge-connected graphs
super-edge-connected graphs
Opis:: Let G be a connected graph with minimum degree δ and edge-connectivity λ. A graph is maximally edge-connected if λ = δ, and it is super-edgeconnected if every minimum edge-cut is trivial; that is, if every minimum edge-cut consists of edges incident with a vertex of minimum degree. The clique number ω(G) of a graph G is the maximum cardinality of a complete subgraph of G. In this paper, we show that a connected graph G with clique number ω(G) ≤ r is maximally edge-connected or super-edge-connected if the number of edges is large enough. These are generalizations of corresponding results for triangle-free graphs by Volkmann and Hong in 2017.
Źródło:: Discussiones Mathematicae Graph Theory; 2019, 39, 2; 567-573
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: Super Edge-Connectivity and Zeroth-Order Randić Index
Autorzy:: He, Zhihong
Lu, Mei
Powiązania:: https://bibliotekanauki.pl/articles/31348172.pdf
Data publikacji:: 2020-11-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: zeroth-order Randić index
super edge-connected
degree
triangle-free graph
minimum degree
Opis:: Define the zeroth-order Randić index as $R^0(G)=∑_{x∈V(G)} \frac{1}{\sqrt{d_G(x)}}$, where $d_G(x)$ denotes the degree of the vertex $x$. In this paper, we present two sufficient conditions for graphs and triangle-free graphs, respectively, to be super edge-connected in terms of the zeroth-order Randić index.
Źródło:: Discussiones Mathematicae Graph Theory; 2020, 40, 4; 971-984
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: A Sufficient Condition for Graphs to Be Super k-Restricted Edge Connected
Autorzy:: Wang, Shiying
Wang, Meiyu
Zhang, Lei
Powiązania:: https://bibliotekanauki.pl/articles/31341790.pdf
Data publikacji:: 2017-08-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: graph
neighborhood
k -restricted edge connectivity
super k -restricted edge connected graph
Opis:: For a subset $S$ of edges in a connected graph $G$, $S$ is a $k$-restricted edge cut if $G − S$ is disconnected and every component of $G − S$ has at least $k$ vertices. The $k$-restricted edge connectivity of $G$, denoted by $ \lambda_k (G) $, is defined as the cardinality of a minimum $k$-restricted edge cut. Let $ \xi_k(G) = \text{min} \{ | [ X , \overline{X} ] | : |X| = k, G[X] $ is connected $ \} $, where $ \overline{X} = V (G) \backslash X $. A graph $G$ is super $k$-restricted edge connected if every minimum $k$-restricted edge cut of $G$ isolates a component of order exactly $k$. Let $k$ be a positive integer and let $G$ be a graph of order $ \nu \ge 2k$. In this paper, we show that if $ | N( u ) \cup N( v ) | \ge k +1 $ for all pairs $u$, $v$ of nonadjacent vertices and $ \xi_k (G) \le \floor{ ν/2}+k $, then $G$ is super $k$-restricted edge connected.
Źródło:: Discussiones Mathematicae Graph Theory; 2017, 37, 3; 537-545
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

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