scholarly journals On the ratio of maximum and minimum degree in maximal intersecting families

2013 ◽  
Vol 313 (2) ◽  
pp. 207-211
Author(s):  
Zoltán Lóránt Nagy ◽  
Lale Özkahya ◽  
Balázs Patkós ◽  
Máté Vizer
Keyword(s):  
Minimum Degree ◽  
Intersecting Families ◽  
Maximum And Minimum Degree

scholarly journals In-situ Desaturation Tests by Electrolysis for Liquefaction Mitigation

2021 ◽  
Author(s):  
Runze Chen ◽  
Yumin Chen ◽  
Hanlong Liu ◽  
Kunxian Zhang ◽  
Ying Zhou ◽  
...  
Keyword(s):  
Minimum Degree ◽  
Electricity Consumption ◽  
Potential Method ◽  
Economic Benefits ◽  
Degree Of Saturation ◽  
Test Results ◽  
Liquefaction Resistance ◽  
The Difference ◽  
Maximum And Minimum Degree

Electrolytic desaturation is a potential method for improving the liquefaction resistance of the liquefiable foundation by reducing the soil saturation. In this study, in-situ desaturation tests were performed to investigate the resistivity of soil at different depth and the water level of the foundation under different current. The test results show that at constant currents of 1 A (Ampere, unit of the direct current), 2 A and 3 A, the saturation of the treated foundation reached 87%, 83% and 80%. During the electrolysis process, the generated gas migrates vertically and horizontally under the influence of buoyancy and gas pressure. In the end of electrolysis, the gas inside the sand foundation basically migrates vertically only. The higher current intensity employed for electrolysis will affect the uniformity and stability of the gas. At constant currents of 1 A, 2 A and 3 A, the difference between the maximum and minimum degree of saturation in the treated foundation was 14%, 18% and 19%; and after electrolysis halted for 144 h, the saturation in the treated foundation was 90%, 85% and 87%. The electricity consumption analysis indicates that the desaturation method has excellent economic benefits in the treatment of saturated sand foundations.

scholarly journals Maximum and Minimum Degree Conditions for Embedding Trees

2020 ◽  
Vol 34 (4) ◽  
pp. 2108-2123
Author(s):  
Guido Besomi ◽  
Matías Pavez-Signé ◽  
Maya Stein
Keyword(s):  
Minimum Degree ◽  
Degree Conditions ◽  
Maximum And Minimum Degree

scholarly journals A note on Huang–Zhao theorem on intersecting families with large minimum degree

2017 ◽  
Vol 340 (5) ◽  
pp. 1098-1103 ◽  
Author(s):  
Peter Frankl ◽  
Norihide Tokushige
Keyword(s):  
Minimum Degree ◽  
Intersecting Families

Degree Kirchhoff Index of Bicyclic Graphs

2017 ◽  
Vol 60 (1) ◽  
pp. 197-205 ◽  
Author(s):  
Zikai Tang ◽  
Hanyuan Deng
Keyword(s):  
Connected Graph ◽  
Minimum Degree ◽  
Kirchhoff Index ◽  
Resistance Distance ◽  
Degree Of Vertex ◽  
Vertex Set ◽  
Maximum And Minimum Degree ◽  
Bicyclic Graphs

AbstractLet G be a connected graph with vertex set V(G).The degree Kirchhoò index of G is defined as S'(G) = Σ{u,v}⊆V(G) d(u)d(v)R(u, v), where d(u) is the degree of vertex u, and R(u, v) denotes the resistance distance between vertices u and v. In this paper, we characterize the graphs having maximum and minimum degree Kirchhoò index among all n-vertex bicyclic graphs with exactly two cycles.

scholarly journals Relations between the energy of graphs and other graph parameters

2021 ◽  
Vol 87 (3) ◽  
pp. 661-672
Author(s):  
Slobodan Filipovski ◽  
Keyword(s):  
Minimum Degree ◽  
Clique Number ◽  
Randić Index ◽  
Randic Index ◽  
Maximum And Minimum Degree ◽  
Graph Parameters

In this paper we give various relations between the energy of graphs and other graph parameters as Randić index, clique number, number of vertices and edges, maximum and minimum degree etc. Moreover, new bounds for the energy of complementary graphs are derived. Our results are based on the concept of vertex energy developed by G. Arizmendi and O. Arizmendi in [Lin. Algebra Appl. doi:10.1016/j.laa.2020.09.025].

scholarly journals The Minimum Number of Nonnegative Edges in Hypergraphs

10.37236/4402 ◽  
2014 ◽  
Vol 21 (3) ◽  
Author(s):  
Hao Huang ◽  
Benny Sudakov
Keyword(s):  
Vector Space ◽  
Minimum Degree ◽  
Constant Factor ◽  
Total Weight ◽  
Real Numbers ◽  
Minimum Number ◽  
Intersecting Families

An $r$-uniform $n$-vertex hypergraph $H$ is said to have the Manickam-Miklós-Singhi (MMS) property if for every assignment of weights to its vertices with nonnegative sum, the number of edges whose total weight is nonnegative is at least the minimum degree of $H$. In this paper we show that for $n>10r^3$, every $r$-uniform $n$-vertex hypergraph with equal codegrees has the MMS property, and the bound on $n$ is essentially tight up to a constant factor. This result has two immediate corollaries. First it shows that every set of $n>10k^3$ real numbers with nonnegative sum has at least $\binom{n-1}{k-1}$ nonnegative $k$-sums, verifying the Manickam-Miklós-Singhi conjecture for this range. More importantly, it implies the vector space Manickam-Miklós-Singhi conjecture which states that for $n \ge 4k$ and any weighting on the $1$-dimensional subspaces of $\mathbb{F}_{q}^n$ with nonnegative sum, the number of nonnegative $k$-dimensional subspaces is at least ${n-1 \brack k-1}_q$. We also discuss two additional generalizations, which can be regarded as analogues of the Erdős-Ko-Rado theorem on $k$-intersecting families.

scholarly journals A note on the vertex-switching reconstruction

1988 ◽  
Vol 11 (4) ◽  
pp. 825-827 ◽  
Author(s):  
I. Krasikov
Keyword(s):  
Minimum Degree ◽  
Maximum And Minimum Degree ◽  
Disconnected Graph

Bounds on the maximum and minimum degree of a graph establishing its reconstructibility from the vertex switching are given. It is also shown that any disconnected graph with at least five vertices is reconstructible.

scholarly journals NEW UPPER BOUND ON THE LARGEST LAPLACIAN EIGENVALUE OF GRAPHS

2020 ◽  
pp. 533
Author(s):  
Hassan Taheri ◽  
Gholam Hossein Fath-Tabar
Keyword(s):  
Randomized Algorithms ◽  
Optimization Problems ◽  
Undirected Graph ◽  
Minimum Degree ◽  
Laplacian Spectrum ◽  
Lower And Upper Bounds ◽  
Laplacian Eigenvalue ◽  
Combinatorial Optimization Problems ◽  
The Past ◽  
Maximum And Minimum Degree

Let G = (V;E) be a simple, undirected graph with maximum and minimum degree ∆ and respectively, and let A be the adjacency matrix and Q be the Laplacianmatrix of G. In the past decades, the Laplacian spectrum has received much more and more attention, since it has been applied to several elds, such as randomized algorithms, combinatorial optimization problems and machine learning. In this paper, we compute lower and upper bounds for the largest Laplacian eigenvalue which is related with a given maximum and minimum degree and a given number of vertices and edges. We also compare our results in this paper with some known results.

Extreme degrees in random subgraphs of regular graphs

1985 ◽  
Vol 97 (1) ◽  
pp. 69-78 ◽  
Author(s):  
Zbigniew Palka
Keyword(s):  
Minimum Degree ◽  
Probability Distributions ◽  
Asymptotic Distributions ◽  
Regular Graphs ◽  
Additional Information ◽  
Initial Graph ◽  
Random Subgraph ◽  
Edge Probability ◽  
Maximum And Minimum Degree ◽  
Random Subgraphs

Let G(d) be a given simple d-regular graph on n labelled vertices, where dn is even. Such a graph will be called an initial graph. Denote by Gp(d) a random subgraph of G(d) obtained by removing edges, each with the same probability q — 1 —p, independently of all other edges (i.e. each edge remains in Gp(d) with probability p). In a recent paper [10] the asymptotic distributions of the number of vertices of a given degree in a random graph Gp(d) were given. The aim of this sequel is to present a wide variety of results devoted to probability distributions of the maximum and minimum degree of Gp(d) with respect to different values of the edge probability p and degree of regularity d. It should be noted here that very detailed results on a similar subject in the case when the initial graph is a complete graph (i.e. when d = n – 1) have already been obtained by Bollobás in the series of papers [2]–[4] (some additional information to the paper [4] was given in [9]). Also, in proving our results we will make use of some ideas given by Bollobás in these papers.

Sign in / Sign up

Export Citation Format

Share Document