Domination Polynomials of certain hexagon lattice graphs

2021 ◽  
Vol 10 (4) ◽  
pp. 723-731
Author(s):  
Caibing Chang ◽  
Haizhen Ren ◽  
Zijian Deng ◽  
Bo Deng
Keyword(s):  
Lattice Graphs

A problem on lattice graphs. Theory and algorithm

Cybernetics ◽  
1981 ◽  
Vol 16 (4) ◽  
pp. 628-631
Author(s):  
L. A. Klygina
Keyword(s):  
Lattice Graphs

scholarly journals Convergence Theorems for Some Layout Measures on Random Lattice and Random Geometric Graphs

2000 ◽  
Vol 9 (6) ◽  
pp. 489-511 ◽  
Author(s):  
JOSEP DÍAZ ◽  
MATHEW D. PENROSE ◽  
JORDI PETIT ◽  
MARÍA SERNA
Keyword(s):  
Constant Factor ◽  
Geometric Graphs ◽  
Convergence Theorems ◽  
Linear Arrangement ◽  
Random Lattice ◽  
Random Geometric Graphs ◽  
Unit Square ◽  
Subcritical Regime ◽  
Probabilistic Setting ◽  
Lattice Graphs

This work deals with convergence theorems and bounds on the cost of several layout measures for lattice graphs, random lattice graphs and sparse random geometric graphs. Specifically, we consider the following problems: Minimum Linear Arrangement, Cutwidth, Sum Cut, Vertex Separation, Edge Bisection and Vertex Bisection. For full square lattices, we give optimal layouts for the problems still open. For arbitrary lattice graphs, we present best possible bounds disregarding a constant factor. We apply percolation theory to the study of lattice graphs in a probabilistic setting. In particular, we deal with the subcritical regime that this class of graphs exhibits and characterize the behaviour of several layout measures in this space of probability. We extend the results on random lattice graphs to random geometric graphs, which are graphs whose nodes are spread at random in the unit square and whose edges connect pairs of points which are within a given distance. We also characterize the behaviour of several layout measures on random geometric graphs in their subcritical regime. Our main results are convergence theorems that can be viewed as an analogue of the Beardwood, Halton and Hammersley theorem for the Euclidean TSP on random points in the unit square.

Characterization of triangular and lattice graphs

1998 ◽  
Vol 39 (5) ◽  
pp. 908-912 ◽  
Author(s):  
V. V. Kabanov
Keyword(s):  
Lattice Graphs

Enumeration of perfect matchings of lattice graphs by Pfaffians

2018 ◽  
Vol 338 ◽  
pp. 412-420
Author(s):  
Xing Feng ◽  
Lianzhu Zhang ◽  
Mingzu Zhang
Keyword(s):  
Perfect Matchings ◽  
Lattice Graphs

Layout Problems on Lattice Graphs

1999 ◽  
pp. 103-112 ◽  
Author(s):  
Josep Díaz ◽  
Mathew D. Penrose ◽  
Jordi Petit ◽  
María Serna
Keyword(s):  
Lattice Graphs

Parallel String Parsing Using Lattice Graphs.

1981 ◽  
Author(s):  
Azriel Rosenfeld
Keyword(s):  
Lattice Graphs

The intrinsic group–subgroup structures of the Diamond and Gyroid minimal surfaces in their conventional unit cells

2022 ◽  
Vol 78 (1) ◽  
Author(s):  
Martin Cramer Pedersen ◽  
Vanessa Robins ◽  
Stephen T. Hyde
Keyword(s):  
Minimal Surfaces ◽  
Subgroup Lattice ◽  
Unit Cells ◽  
Lattice Graphs ◽  
Conventional Unit

The intrinsic, hyperbolic crystallography of the Diamond and Gyroid minimal surfaces in their conventional unit cells is introduced and analysed. Tables are constructed of symmetry subgroups commensurate with the translational symmetries of the surfaces as well as group–subgroup lattice graphs.

Hamiltonian Tours and Paths in Rectangular Lattice Graphs

1977 ◽  
Vol 50 (3) ◽  
pp. 147-150 ◽  
Author(s):  
Gerald L. Thompson
Keyword(s):  
Rectangular Lattice ◽  
Lattice Graphs
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