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 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 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).

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 Peg Solitaire on Cartesian Products of Graphs

2021 ◽  
Vol 37 (3) ◽  
pp. 907-917
Author(s):  
Martin Kreh ◽  
Jan-Hendrik de Wiljes
Keyword(s):  
Cartesian Product ◽  
Cartesian Products ◽  
Connected Graphs ◽  
Grid Graphs ◽  
Cartesian Products Of Graphs

AbstractIn 2011, Beeler and Hoilman generalized the game of peg solitaire to arbitrary connected graphs. In the same article, the authors proved some results on the solvability of Cartesian products, given solvable or distance 2-solvable graphs. We extend these results to Cartesian products of certain unsolvable graphs. In particular, we prove that ladders and grid graphs are solvable and, further, even the Cartesian product of two stars, which in a sense are the “most” unsolvable graphs.

scholarly journals A linear-time algorithm for the longest path problem in rectangular grid graphs

2012 ◽  
Vol 160 (3) ◽  
pp. 210-217 ◽  
Author(s):  
Fatemeh Keshavarz-Kohjerdi ◽  
Alireza Bagheri ◽  
Asghar Asgharian-Sardroud
Keyword(s):  
Linear Time ◽  
Time Algorithm ◽  
Linear Time Algorithm ◽  
Rectangular Grid ◽  
Grid Graphs ◽  
Longest Path ◽  
Longest Path Problem

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
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