scholarly journals A Note on Inhomogeneous Percolation on Ladder Graphs

2019 ◽  
Vol 51 (3) ◽  
pp. 827-833
Author(s):  
Bernardo N. B. de Lima ◽  
Humberto C. Sanna
Keyword(s):  
Inhomogeneous Percolation ◽  
Ladder Graphs

scholarly journals Inhomogeneous Percolation on Ladder Graphs

2019 ◽  
Vol 33 (2) ◽  
pp. 992-1010 ◽  
Author(s):  
Réka Szabó ◽  
Daniel Valesin
Keyword(s):  
Inhomogeneous Percolation ◽  
Ladder Graphs

scholarly journals Sharpness for inhomogeneous percolation on quasi-transitive graphs

2019 ◽  
Vol 152 ◽  
pp. 28-34
Author(s):  
Thomas Beekenkamp ◽  
Tim Hulshof
Keyword(s):  
Inhomogeneous Percolation ◽  
Transitive Graphs

scholarly journals Topological invariants for the line graphs of some classes of graphs

2019 ◽  
Vol 17 (1) ◽  
pp. 1483-1490
Author(s):  
Xiaoqing Zhou ◽  
Mustafa Habib ◽  
Tariq Javeed Zia ◽  
Asim Naseem ◽  
Anila Hanif ◽  
...  
Keyword(s):  
Communication Theory ◽  
Chemical Reactivity ◽  
Line Graph ◽  
Chemical Properties ◽  
Topological Invariants ◽  
Line Graphs ◽  
Physical And Chemical Properties ◽  
Physical And Chemical ◽  
Ladder Graphs ◽  
And Chemical Properties

AbstractGraph theory plays important roles in the fields of electronic and electrical engineering. For example, it is critical in signal processing, networking, communication theory, and many other important topics. A topological index (TI) is a real number attached to graph networks and correlates the chemical networks with physical and chemical properties, as well as with chemical reactivity. In this paper, our aim is to compute degree-dependent TIs for the line graph of the Wheel and Ladder graphs. To perform these computations, we first computed M-polynomials and then from the M-polynomials we recovered nine degree-dependent TIs for the line graph of the Wheel and Ladder graphs.

High-energy behaviour of ladder graphs with multiple loops

1971 ◽  
Vol 2 (22) ◽  
pp. 1146-1148 ◽  
Author(s):  
Z. Horváth ◽  
G. Pócsik
Keyword(s):  
High Energy ◽  
Energy Behaviour ◽  
Ladder Graphs

scholarly journals On The Radio Antipodal Mean Number of Certain Types of Ladder Graphs

2020 ◽  
Vol 09 (06) ◽  
pp. 4607-4614
Author(s):  
Kins Yenoke ◽  
Arputha Jose T ◽  
Venugopal P
Keyword(s):  
Ladder Graphs

Virial expansion for a polymer chain: the two parameter approximation

1979 ◽  
Vol 367 (1729) ◽  
pp. 143-174 ◽  
Keyword(s):  
Gaussian Model ◽  
Dominant Term ◽  
Cubic Lattices ◽  
Functional Relations ◽  
Ladder Graph ◽  
Simple Rules ◽  
The Mean ◽  
Parameter Approximation ◽  
Ladder Graphs ◽  
Two Parameter

A complete diagrammatic expansion is developed for the Domb-Joyce model of an N -step chain, with an interaction w which varies between 0 and 1. Simple rules are given for obtaining the diagrams. The correspondence between these diagrams and appropriate generating functions permits computation of the coefficients of the series α 2 N ( w ) = 1 + k 1 w + k 2 w 2 + . . ., where α 2 N ( w ) is the expansion factor of the mean square end-to-end length of the chain. The dominant term in N of each of the first three k r is shown to be identical for the three cubic lattices and for the Gaussian continuum model, with the exception of a scale factor h 0 . Retention of only this dominant term yields a ‘two-parameter’ expansion equivalent to that of Zimm (1946), Fixman (1955) and others. Diagrams are classed either as ladder or as non-ladder graphs. The ladder graph contributions are summed by using functional relations of Domb & Joyce (1972). The non-ladder contributions for the first three coefficients are computed individually, thereby yielding results for k 1 , k 2 and k 3 in terms of the ‘universal’ parameter z = h 0 N 1/2 w . The terms k 1 and k 2 agree with previous computations for the Gaussian model but k 3 differs slightly.

scholarly journals Spectral bounds in random graphs applied to spreading phenomena and percolation

2018 ◽  
Vol 50 (2) ◽  
pp. 480-503
Author(s):  
Rémi Lemonnier ◽  
Kevin Scaman ◽  
Nicolas Vayatis
Keyword(s):  
Spectral Radius ◽  
Random Graphs ◽  
Reachable Sets ◽  
Positive Correlation ◽  
Subcritical Regime ◽  
Independent Cascade Model ◽  
Inhomogeneous Percolation ◽  
Independent Cascade ◽  
Spectral Bounds

Abstract In this paper we derive nonasymptotic upper bounds for the size of reachable sets in random graphs. These bounds are subject to a phase transition phenomenon triggered by the spectral radius of the hazard matrix, a reweighted version of the adjacency matrix. Such bounds are valid for a large class of random graphs, called local positive correlation (LPC) random graphs, displaying local positive correlation. In particular, in our main result we state that the size of reachable sets in the subcritical regime for LPC random graphs is at most of order O(√n), where n is the size of the network, and of order O(n2/3) in the critical regime, where the epidemic thresholds are driven by the size of the spectral radius of the hazard matrix with respect to 1. As a corollary, we also show that such bounds hold for the size of the giant component in inhomogeneous percolation, the SIR model in epidemiology, as well as for the long-term influence of a node in the independent cascade model.

scholarly journals CHORD DIAGRAMS AND BPHZ SUBTRACTIONS

1996 ◽  
Vol 11 (13) ◽  
pp. 1095-1105 ◽  
Author(s):  
IOANNIS TSOHANTJIS ◽  
ALEX C. KALLONIATIS ◽  
PETER D. JARVIS ◽  
GEORGE THOMPSON
Keyword(s):  
Field Theory ◽  
Knot Theory ◽  
Equivalence Relations ◽  
Quantum Field ◽  
Subtraction Scheme ◽  
Chord Diagrams ◽  
Point Vertex ◽  
Fundamental Relationship ◽  
Perturbative Quantum ◽  
Ladder Graphs

The combinatorics of the BPHZ subtraction scheme for a class of ladder graphs for the three-point vertex in ɸ3 theory is transcribed into certain connectivity relations for marked chord diagrams (knots with transversal intersections). The resolution of the singular crossings using the equivalence relations in these examples provides confirmation of a proposed fundamental relationship between knot theory and renormalization in perturbative quantum field theory.

scholarly journals Orientable biembeddings of cyclic Steiner triple systems from current assignments on Möbius ladder graphs

2009 ◽  
Vol 309 (9) ◽  
pp. 2847-2860 ◽  
Author(s):  
M.J. Grannell ◽  
V.P. Korzhik
Keyword(s):  
Steiner Triple Systems ◽  
Triple Systems ◽  
Ladder Graphs
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