scholarly journals On a problem of Ahlswede and Katona

2009 ◽  
Vol 46 (3) ◽  
pp. 423-435
Author(s):  
Stephan Wagner ◽  
Hua Wang
Keyword(s):  
Complete Graph ◽  
Simple Graphs

Let p ( G ) denote the number of pairs of adjacent edges in a graph G . Ahlswede and Katona considered the problem of maximizing p ( G ) over all simple graphs with a given number n of vertices and a given number N of edges. They showed that p ( G ) is either maximized by a quasi-complete graph or by a quasi-star. They also studied the range of N (depending on n ) for which the quasi-complete graph is superior to the quasi-star (and vice versa) and formulated two questions on distributions in this context. This paper is devoted to the solution of these problems.

New Bounds on the List-Chromatic Index of the Complete Graph and Other Simple Graphs

1997 ◽  
Vol 6 (3) ◽  
pp. 295-313 ◽  
Author(s):  
ROLAND HÄGGKVIST ◽  
JEANNETTE JANSSEN
Keyword(s):  
Complete Graph ◽  
Maximum Degree ◽  
Simple Graph ◽  
Asymptotic Result ◽  
Complete Graphs ◽  
Chromatic Index ◽  
Simple Graphs ◽  
Odd Order

In this paper we show that the list chromatic index of the complete graph Kn is at most n. This proves the list-chromatic conjecture for complete graphs of odd order. We also prove the asymptotic result that for a simple graph with maximum degree d the list chromatic index exceeds d by at most [Oscr ](d2/3√log d).

scholarly journals Birth–death fixation probabilities for structured populations

2013 ◽  
Vol 469 (2153) ◽  
pp. 20120248 ◽  
Author(s):  
Burton Voorhees
Keyword(s):  
Complete Graph ◽  
Present Model ◽  
Automorphism Groups ◽  
Linear Equations ◽  
Structured Populations ◽  
Edge Weight ◽  
Simple Graphs ◽  
Fixation Probabilities ◽  
Fitness Parameter ◽  
Birth Death

This paper presents an adaptation of the Moran birth–death model of evolutionary processes on graphs. The present model makes use of the full population state space consisting of 2 N binary-valued vectors, and a Markov process on this space with a transition matrix defined by the edge weight matrix for any given graph. While the general case involves solution of 2 N – 2 linear equations, symmetry considerations substantially reduce this for graphs with large automorphism groups, and a number of simple examples are considered. A parameter called graph determinacy is introduced, measuring the extent to which the fate of any randomly chosen population state is determined. Some simple graphs that suppress or enhance selection are analysed, and comparison of several examples to the Moran process on a complete graph indicates that in some cases a graph may enhance selection relative to a complete graph for only limited values of the fitness parameter.

Super Graceful Labeling for Some Simple Graphs

2012 ◽  
Vol 2 (1) ◽  
pp. 35 ◽  
Author(s):  
M. A. Perumal ◽  
S. Navaneethakrishnan ◽  
A. Nagaraja ◽  
S. Arockiaraj
Keyword(s):  
Graceful Labeling ◽  
Simple Graphs

scholarly journals On the Generalized Distance Energy of Graphs

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 17 ◽  
Author(s):  
Abdollah Alhevaz ◽  
Maryam Baghipur ◽  
Hilal A. Ganie ◽  
Yilun Shang
Keyword(s):  
Lower Bounds ◽  
Complete Graph ◽  
Connected Graph ◽  
Distance Matrix ◽  
Wiener Index ◽  
Diagonal Matrix ◽  
Upper And Lower Bounds ◽  
Star Graph ◽  
Extremal Graphs ◽  
Generalized Distance

The generalized distance matrix D α ( G ) of a connected graph G is defined as D α ( G ) = α T r ( G ) + ( 1 − α ) D ( G ) , where 0 ≤ α ≤ 1 , D ( G ) is the distance matrix and T r ( G ) is the diagonal matrix of the node transmissions. In this paper, we extend the concept of energy to the generalized distance matrix and define the generalized distance energy E D α ( G ) . Some new upper and lower bounds for the generalized distance energy E D α ( G ) of G are established based on parameters including the Wiener index W ( G ) and the transmission degrees. Extremal graphs attaining these bounds are identified. It is found that the complete graph has the minimum generalized distance energy among all connected graphs, while the minimum is attained by the star graph among trees of order n.

scholarly journals On the Second-Largest Reciprocal Distance Signless Laplacian Eigenvalue

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 512
Author(s):  
Maryam Baghipur ◽  
Modjtaba Ghorbani ◽  
Hilal A. Ganie ◽  
Yilun Shang
Keyword(s):  
Lower Bounds ◽  
Complete Graph ◽  
Distance Matrix ◽  
Upper And Lower Bounds ◽  
Laplacian Eigenvalue ◽  
Signless Laplacian ◽  
Graph Parameters ◽  
Simple Connected Graph ◽  
Second Largest Eigenvalue ◽  
Reciprocal Distance Matrix

The signless Laplacian reciprocal distance matrix for a simple connected graph G is defined as RQ(G)=diag(RH(G))+RD(G). Here, RD(G) is the Harary matrix (also called reciprocal distance matrix) while diag(RH(G)) represents the diagonal matrix of the total reciprocal distance vertices. In the present work, some upper and lower bounds for the second-largest eigenvalue of the signless Laplacian reciprocal distance matrix of graphs in terms of various graph parameters are investigated. Besides, all graphs attaining these new bounds are characterized. Additionally, it is inferred that among all connected graphs with n vertices, the complete graph Kn and the graph Kn−e obtained from Kn by deleting an edge e have the maximum second-largest signless Laplacian reciprocal distance eigenvalue.

scholarly journals Undirected Complete Graph to Design New Public Key Cryptosystem

2021 ◽  
Vol 1897 (1) ◽  
pp. 012045
Author(s):  
Karrar Taher R. Aljamaly ◽  
Ruma Kareem K. Ajeena
Keyword(s):  
Complete Graph ◽  
Public Key ◽  
Public Key Cryptosystem ◽  
New Public

scholarly journals Turán theorems for unavoidable patterns

2021 ◽  
pp. 1-20
Author(s):  
ANTÓNIO GIRÃO ◽  
BHARGAV NARAYANAN
Keyword(s):  
Complete Graph ◽  
Blow Up ◽  
Ramsey Numbers ◽  
Order Of Magnitude ◽  
Transitive Tournament ◽  
Unavoidable Patterns

Abstract We prove Turán-type theorems for two related Ramsey problems raised by Bollobás and by Fox and Sudakov. First, for t ≥ 3, we show that any two-colouring of the complete graph on n vertices that is δ-far from being monochromatic contains an unavoidable t-colouring when δ ≫ n−1/t, where an unavoidable t-colouring is any two-colouring of a clique of order 2t in which one colour forms either a clique of order t or two disjoint cliques of order t. Next, for t ≥ 3, we show that any tournament on n vertices that is δ-far from being transitive contains an unavoidable t-tournament when δ ≫ n−1/[t/2], where an unavoidable t-tournament is the blow-up of a cyclic triangle obtained by replacing each vertex of the triangle by a transitive tournament of order t. Conditional on a well-known conjecture about bipartite Turán numbers, both our results are sharp up to implied constants and hence determine the order of magnitude of the corresponding off-diagonal Ramsey numbers.

Design Criteria for Safer Manual Lifting by Men and Women

1982 ◽  
Vol 26 (6) ◽  
pp. 503-507
Author(s):  
Dudley G. Letbetter
Keyword(s):  
Muscle Fatigue ◽  
Material Handling ◽  
Human Anatomy ◽  
Design Criteria ◽  
Maximum Weight ◽  
Manual Lifting ◽  
Men And Women ◽  
Simple Graphs ◽  
Cardiovascular Capacity ◽  
Specific Material

Simplified design criteria are provided for two-handed, manual lifting by standing men and women, without selective assignment of personnel to specific material handling tasks. Based on a 1981 NIOSH report, application of these criteria requires no knowledge of human anatomy, anthropometry, biomechanics, psychophysics, muscle fatigue, cardiovascular capacity, or metabolic endurance. A person who can read and use simple graphs can quickly determine the maximum weight of a lifted object. The information needed is the horizontal grasp distance and the initial grasp height and lift distance of the object, plus the frequency and duration of lifting.

scholarly journals A property of the colored complete graph

1979 ◽  
Vol 25 (2) ◽  
pp. 175-178 ◽  
Author(s):  
J. Shearer
Keyword(s):  
Complete Graph

On the pseudoachromatic index of the complete graph

2010 ◽  
Vol 66 (2) ◽  
pp. 89-97 ◽  
Author(s):  
M. Gabriela Araujo-Pardo ◽  
Juan José Montellano-Ballesteros ◽  
Ricardo Strausz
Keyword(s):  
Complete Graph
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