Temat: edge - Prolib Integro

Skocz do pozycji: 1.

Tytuł:: Maximum Edge-Colorings Of Graphs
Autorzy:: Jendrol’, Stanislav
Vrbjarová, Michaela
Tematy:: edge-coloring
r -maximum k -edge-coloring
unique-maximum edge-coloring
weak-odd edge-coloring
weak-even edge-coloring; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/31341153.pdf Link otwiera się w nowym oknie
Opis:: An $r$-maximum $k$-edge-coloring of $G$ is a $k$-edge-coloring of $G$ having a property that for every vertex $v$ of degree $d_G(v) = d, d \ge r$, the maximum color, that is present at vertex $v$, occurs at $v$ exactly $r$ times. The $r$-maximum index $ \chi_r^′ (G) $ is defined to be the minimum number $k$ of colors needed for an $r$-maximum $k$-edge-coloring of graph $G$. In this paper we show that $ \chi_r^′ (G) \le 3 $ for any nontrivial connected graph $G$ and $ r = 1$ or 2. The bound 3 is tight. All graphs $G$ with $ \chi_1^' (G) =i $, $i = 1, 2, 3$ are characterized. The precise value of the $r$-maximum index, $ r \ge 1 $, is determined for trees and complete graphs.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: Median of a graph with respect to edges
Autorzy:: Santhakumaran, A.
Tematy:: median
vertex-to-edge median
edge-to-vertex median
edge-to-edge median; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/743645.pdf Link otwiera się w nowym oknie
Opis:: For any vertex v and any edge e in a non-trivial connected graph G, the distance sum d(v) of v is $d(v) = ∑_{u ∈ V}d(v,u)$, the vertex-to-edge distance sum d₁(v) of v is $d₁(v) = ∑_{e ∈ E}d(v,e)$, the edge-to-vertex distance sum d₂(e) of e is $d₂(e) = ∑_{v ∈ V}d(e,v)$ and the edge-to-edge distance sum d₃(e) of e is $d₃(e) = ∑_{f ∈ E}d(e,f)$. The set M(G) of all vertices v for which d(v) is minimum is the median of G; the set M₁(G) of all vertices v for which d₁(v) is minimum is the vertex-to-edge median of G; the set M₂(G) of all edges e for which d₂(e) is minimum is the edge-to-vertex median of G; and the set M₃(G) of all edges e for which d₃(e) is minimum is the edge-to-edge median of G. We determine these medians for some classes of graphs. We prove that the edge-to-edge median of a graph is the same as the median of its line graph. It is shown that the center and the median; the vertex-to-edge center and the vertex-to-edge median; the edge-to-vertex center and the edge-to-vertex median; and the edge-to-edge center and the edge-to-edge median of a graph are not only different but can be arbitrarily far apart.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 3.

Tytuł:: The upper edge geodetic number and the forcing edge geodetic number of a graph
Autorzy:: Santhakumaran, A. P.
John, J.
Tematy:: geodetic number
edge geodetic basis
edge geodetic number
upper edge geodetic number
forcing edge geodetic number; Pokaż więcej
Wydawca:: Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Powiązania:: https://bibliotekanauki.pl/articles/255845.pdf Link otwiera się w nowym oknie
Opis:: An edge geodetic set of a connected graph G of order p ≥ 2 is a set S ⊆ V(G) such that every edge of G is contained in a geodesic joining some pair of vertices in S. The edge geodetic number g1(G) of G is the minimum cardinality of its edge geodetic sets and any edge geodetic set of cardinality g1(G) is a minimum edge geodetic set of G or an edge geodetic basis of G. An edge geodetic set S in a connected graph G is a minimal edge geodetic set if no proper subset of S is an edge geodetic set of G. The upper edge geodetic number g1+(G) of G is the maximum cardinality of a minimal edge geodetic set of G. The upper edge geodetic number of certain classes of graphs are determined. It is shown that for every two integers a and b such that 2 ≤ a ≤ b, there exists a connected graph G with g1(G) = a and g1+(G) = b. For an edge geodetic basis S of G, a subset T ⊆ S is called a forcing subset for S if S is the unique edge geodetic basis containing T. A forcing subset for S of minimum cardinality is a minimum forcing subset of S. The forcing edge geodetic number of S denoted by ƒ1(S), is the cardinality of a minimum forcing subset of S. The forcing edge geodetic number of G, denoted by ƒ1(G), is ƒ1(G) = min{ ƒ1(S)}, where the minimum is taken over all edge geodetic bases S in G. Some general properties satisfied by this concept are studied. The forcing edge geodetic number of certain classes of graphs are determined. It is shown that for every pair a, b of integers with 0 ≤ a < b and b ≥ 2, there exists a connected graph G such thatƒ1(G) = a and g1(G) = b.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 4.

Tytuł:: Sufficient Conditions for Maximally Edge-Connected and Super-Edge-Connected Graphs Depending on The Clique Number
Autorzy:: Volkmann, Lutz
Tematy:: edge-connectivity
clique number
maximally edge-connected graphs
super-edge-connected graphs; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/31343389.pdf Link otwiera się w nowym oknie
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.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 5.

Tytuł:: On edge detour graphs
Autorzy:: Santhakumaran, A.P.
Athisayanathan, S.
Tematy:: detour
edge detour set
edge detour basis
edge detour number; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/744551.pdf Link otwiera się w nowym oknie
Opis:: For two vertices u and v in a graph G = (V,E), the detour distance D(u,v) is the length of a longest u-v path in G. A u-v path of length D(u,v) is called a u-v detour. A set S ⊆V is called an edge detour set if every edge in G lies on a detour joining a pair of vertices of S. The edge detour number dn₁(G) of G is the minimum order of its edge detour sets and any edge detour set of order dn₁(G) is an edge detour basis of G. A connected graph G is called an edge detour graph if it has an edge detour set. It is proved that for any non-trivial tree T of order p and detour diameter D, dn₁(T) ≤ p-D+1 and dn₁(T) = p-D+1 if and only if T is a caterpillar. We show that for each triple D, k, p of integers with 3 ≤ k ≤ p-D+1 and D ≥ 4, there is an edge detour graph G of order p with detour diameter D and dn₁(G) = k. We also show that for any three positive integers R, D, k with k ≥ 3 and R < D ≤ 2R, there is an edge detour graph G with detour radius R, detour diameter D and dn₁(G) = k. Edge detour graphs G with detour diameter D ≤ 4 are characterized when dn₁(G) = p-2 or dn₁(G) = p-1.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 6.

Tytuł:: The edge geodetic number and Cartesian product of graphs
Autorzy:: Santhakumaran, A.
Ullas Chandran, S.
Tematy:: geodetic number
edge geodetic number
linear edge geodetic set
perfect edge geodetic set
(edge, vertex)-geodetic set
superior edge geodetic set; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/744517.pdf Link otwiera się w nowym oknie
Opis:: For a nontrivial connected graph G = (V(G),E(G)), a set S⊆ V(G) is called an edge geodetic set of G if every edge of G is contained in a geodesic joining some pair of vertices in S. The edge geodetic number g₁(G) of G is the minimum order of its edge geodetic sets. Bounds for the edge geodetic number of Cartesian product graphs are proved and improved upper bounds are determined for a special class of graphs. Exact values of the edge geodetic number of Cartesian product are obtained for several classes of graphs. Also we obtain a necessary condition of G for which g₁(G ☐ K₂) = g₁(G).
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 7.

Tytuł:: On the independence number of edge chromatic critical graphs
Autorzy:: Pang, Shiyou
Miao, Lianying
Song, Wenyao
Miao, Zhengke
Tematy:: edge coloring
edge-chromatic critical graphs
independence number; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/30148675.pdf Link otwiera się w nowym oknie
Opis:: In 1968, Vizing conjectured that for any edge chromatic critical graph $G = (V,E)$ with maximum degree $△$ and independence number $α(G)$, $α(G) ≤ \frac{|V|}{2}$. It is known that $α(G) < \frac{3∆−2}{5∆−2}|V|$. In this paper we improve this bound when $△≥4$. Our precise result depends on the number $n_2$ of 2-vertices in $G$, but in particular we prove that $α(G) ≤\frac{3∆−3}{5∆−3}|V|$ when $△≥5$ and $n_2≤2(△− 1)$.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 8.

Tytuł:: Mitral valve surgery for persistent or recurrent mitral regurgitation after transcatheter edge-to-edge repair is associated with improved survival
Autorzy:: Mazur, Piotr
El Shaer, Ahmed
Arghami, Arman
Eleid, Mackram F.
Greason, Kevin
Chavez Ponce, Alejandra
Crestanello, Juan A.
Guerrero, Mayra
Alkhouli, Mohamad
Rihal, Charanjit S.
Opis:: Background: The management of severe mitral regurgitation (MR) after transcatheter edge‐to‐edge repair (TEER) remains a clinical conundrum. Considering the growing volume of TEER, more outcomes data for mitral surgery in this cohort are needed. Methods and Results: Symptomatic patients with persistent or recurrent severe MR after TEER evaluated between May 2014 and June 2021 were included. The primary outcome was all‐cause mortality in patients who were treated with surgery versus medical therapy. The Kaplan–Meier and Cox regression methods were used to report risk‐adjusted survival analyses. Among the 142 included patients, 44 (31.0%) underwent mitral surgery. Patients who underwent surgery were younger than those treated medically (74.1±8.9 versus 78.6±10.5 years, P=0.01). Major comorbidities were similar except obesity, sleep apnea, left ventricular dimensions, and ejection fraction. Society of Thoracic Surgeons Predicted Risk of Operative Mortality was 9.0±4.7 versus 7.9±4.9 in the surgical versus medical therapy groups, respectively, P=0.22. Time from TEER to detection of severe MR was similar in both groups (median [interquartile range] 97.5 [39.5–384] versus 93.5 [40–389] days in the surgical versus medical groups, respectively [P>0.05]). In the surgical group, valve replacement was performed in all patients. Operative mortality was 4.5% (observed/expected ratio 0.55), and major complications were uncommon. After risk‐adjustment, surgery was associated with significantly lower all‐cause mortality (adjusted hazard ratio, 0.33 [95% CI, 0.12–0.92], P=0.001) compared with medial therapy.: Conclusions: Compared with medical therapy, mitral surgery in patients with severe persistent or recurrent MR after TEER is associated with lower mortality despite the high‐risk profile of these patients. Patients with severe MR after TEER should be considered for surgery at a referral mitral surgical center.
Dostawca treści:: Repozytorium Uniwersytetu Jagiellońskiego

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Skocz do pozycji: 9.

Tytuł:: On the ρ-Edge Stability Number of Graphs
Autorzy:: Kemnitz, Arnfried
Marangio, Massimiliano
Tematy:: edge stability number
line stability
invariant
chromatic edge stability index
chromatic index
edge coloring; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/32361738.pdf Link otwiera się w nowym oknie
Opis:: For an arbitrary invariant $ \rho(G) $ of a graph $G$ the $ \rho $-edge stability number $ es_\rho (G) $ is the minimum number of edges of $G$ whose removal results in a graph $ H \subseteq G $ with $ \rho (H) \ne \rho (G) $ or with $ E(H) = \emptyset $. In the first part of this paper we give some general lower and upper bounds for the $ \rho $-edge stability number. In the second part we study the $ \chi^' $-edge stability number of graphs, where $ \chi^' = \chi^' (G) $ is the chromatic index of $G$. We prove some general results for the so-called chromatic edge stability index $ es_{ \chi^′ } (G) $ and determine $ es_{ \chi^′ } (G) $ exactly for specific classes of graphs.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 10.

Tytuł:: Graphs with Large Generalized (Edge-)Connectivity
Autorzy:: Li, Xueliang
Mao, Yaping
Tematy:: (edge-)connectivity
Steiner tree
internally disjoint trees
edge-disjoint trees
packing
generalized (edge-)connectivity; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/31340594.pdf Link otwiera się w nowym oknie
Opis:: The generalized $k$-connectivity $ \kappa_k (G) $ of a graph $G$, introduced by Hager in 1985, is a nice generalization of the classical connectivity. Recently, as a natural counterpart, we proposed the concept of generalized $k$-edge-connectivity $ \lambda_k (G)$. In this paper, graphs of order $n$ such that $ \kappa_k (G) = n - k/2 - 1 $ and $ \lambda_k (G) = n - k/2 - 1 $ for even $k$ are characterized.
Dostawca treści:: Biblioteka Nauki

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