On Independent Vertex Sets in Subclasses of Apple-Free Graphs

Algorithmica ◽  
2008 ◽  
Vol 56 (4) ◽  
pp. 383-393 ◽  
Author(s):  
Andreas Brandstädt ◽  
Tilo Klembt ◽  
Vadim V. Lozin ◽  
Raffaele Mosca
Keyword(s):  
Independent Vertex ◽  
Vertex Sets

scholarly journals The Minimum Merrifield–Simmons Index of Unicyclic Graphs with Diameter at Most Four

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Kun Zhao ◽  
Shangzhao Li ◽  
Shaojun Dai
Keyword(s):  
Unicyclic Graphs ◽  
Independent Vertex ◽  
Vertex Set ◽  
Vertex Sets

The Merrifield–Simmons index i G of a graph G is defined as the number of subsets of the vertex set, in which any two vertices are nonadjacent, i.e., the number of independent vertex sets of G . In this paper, we determine the minimum Merrifield–Simmons index of unicyclic graphs with n vertices and diameter at most four.

scholarly journals Enumerating independent vertex sets in grid graphs

2016 ◽  
Vol 510 ◽  
pp. 192-204 ◽  
Author(s):  
Seungsang Oh ◽  
Sangyop Lee
Keyword(s):  
Grid Graphs ◽  
Independent Vertex ◽  
Vertex Sets

scholarly journals The Merrifield-Simmons Index and Hosoya Index ofC(n,k,λ)Graphs

2012 ◽  
Vol 2012 ◽  
pp. 1-8
Author(s):  
Shaojun Dai ◽  
Ruihai Zhang
Keyword(s):  
Hosoya Index ◽  
Independent Vertex ◽  
Vertex Set ◽  
Independent Edge ◽  
Vertex Sets

The Merrifield-Simmons indexi(G)of a graphGis defined as the number of subsets of the vertex set, in which any two vertices are nonadjacent, that is, the number of independent vertex sets ofGThe Hosoya indexz(G)of a graphGis defined as the total number of independent edge subsets, that is, the total number of its matchings. ByC(n,k,λ)we denote the set of graphs withnvertices,kcycles, the length of every cycle isλ, and all the edges not on the cycles are pendant edges which are attached to the same vertex. In this paper, we investigate the Merrifield-Simmons indexi(G)and the Hosoya indexz(G)for a graphGinC(n,k,λ).

scholarly journals Approximating minimum feedback vertex sets in hypergraphs

2000 ◽  
Vol 246 (1-2) ◽  
pp. 107-116 ◽  
Author(s):  
Toshihiro Fujito
Keyword(s):  
Vertex Sets

Analysis of Critical and Redundant Vertices in Controlling Directed Complex Networks Using Feedback Vertex Sets

2018 ◽  
Vol 25 (10) ◽  
pp. 1071-1090 ◽  
Author(s):  
Yu Bao ◽  
Morihiro Hayashida ◽  
Pengyu Liu ◽  
Masayuki Ishitsuka ◽  
Jose C. Nacher ◽  
...  
Keyword(s):  
Complex Networks ◽  
Vertex Sets

scholarly journals Topological Infinite Gammoids, and a New Menger-Type Theorem for Infinite Graphs

10.37236/6083 ◽  
2018 ◽  
Vol 25 (3) ◽  
Author(s):  
Johannes Carmesin
Keyword(s):  
Type Theorem ◽  
Main Tool ◽  
Infinite Graphs ◽  
Disjoint Paths ◽  
Natural Topology ◽  
Locally Finite ◽  
Finite Graphs ◽  
Locally Finite Graphs ◽  
Vertex Sets ◽  
Special Case

Answering a question of Diestel, we develop a topological notion of gammoids in infinite graphs which, unlike traditional infinite gammoids, always define a matroid.As our main tool, we prove for any infinite graph $G$ with vertex-sets $A$ and $B$, if every finite subset of $A$ is linked to $B$ by disjoint paths, then the whole of $A$ can be linked to the closure of $B$ by disjoint paths or rays in a natural topology on $G$ and its ends.This latter theorem implies the topological Menger theorem of Diestel for locally finite graphs. It also implies a special case of the infinite Menger theorem of Aharoni and Berger.

MINIMUM WEIGHT FEEDBACK VERTEX SETS IN CIRCLE n-GON GRAPHS AND CIRCLE TRAPEZOID GRAPHS

2011 ◽  
Vol 03 (03) ◽  
pp. 323-336 ◽  
Author(s):  
FANICA GAVRIL
Keyword(s):  
Minimum Weight ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Circle Graphs ◽  
Intersection Model ◽  
The Family ◽  
Positive Weights ◽  
Vertex Set ◽  
Vertex Sets ◽  
Trapezoid Graphs

A circle n-gon is the region between n or fewer non-crossing chords of a circle, no chord connecting the arcs between two other chords; the sides of a circle n-gon are either chords or arcs of the circle. A circle n-gon graph is the intersection graph of a family of circle n-gons in a circle. The family of circle trapezoid graphs is exactly the family of circle 2-gon graphs and the family of circle graphs is exactly the family of circle 1-gon graphs. The family of circle n-gon graphs contains the polygon-circle graphs which have an intersection representation by circle polygons, each polygon with at most n chords. We describe a polynomial time algorithm to find a minimum weight feedback vertex set, or equivalently, a maximum weight induced forest, in a circle n-gon graph with positive weights, when its intersection model by n-gon-interval-filaments is given.

scholarly journals Limit theorems for isotropic random walks on triangle buildings

2002 ◽  
Vol 73 (3) ◽  
pp. 301-334 ◽  
Author(s):  
Marc Lindlbauer ◽  
Michael Voit
Keyword(s):  
Limit Theorem ◽  
Random Walks ◽  
Local Limit Theorem ◽  
Local Limit ◽  
Two Dimensional ◽  
Littlewood Polynomials ◽  
Large Numbers ◽  
Moment Functions ◽  
Vertex Sets ◽  
Isotropic Random

AbstractThe spherical functions of triangle buildings can be described in terms of certain two-dimensional orthogonal polynomials on Steiner's hypocycloid which are closely related to Hall-Littlewood polynomials. They lead to a one-parameter family of two-dimensional polynimial hypergroups. In this paper we investigate isotropic random walks on the vertex sets of triangle buildings in terms of their projections to these hypergroups. We present strong laws of large numbers, a central limit theorem, and a local limit theorem; all these results are well-known for homogeneous trees. Proofs are based on moment functions on hypergroups and on explicit expansions of the hypergroup characters in terms of certain two-dimensional Tchebychev polynimials.

Sign in / Sign up

Export Citation Format

Share Document