Results 1 to 10 of about 2,448,104 (66)

𝕮-inverse of graphs and mixed graphs

Open Mathematics
This article introduces a generalization of the concept of inverse graphs applicable to both graphs and mixed graphs. Given a graph GG with adjacency matrix A(G)A\left(G), the inverse graph G−1{G}^{-1} is defined such that its adjacency matrix is similar
Alomari Omar, Abudayah Mohammad, Ghanem Manal   +2 more
doaj   +2 more sources

The number of satisfying assignments of random 2‐SAT formulas

Random Structures &Algorithms, Volume 58, Issue 4, Page 609-647, July 2021., 2021
Abstract We show that throughout the satisfiable phase the normalized number of satisfying assignments of a random 2‐SAT formula converges in probability to an expression predicted by the cavity method from statistical physics. The proof is based on showing that the Belief Propagation algorithm renders the correct marginal probability that a variable ...
Dimitris Achlioptas, Amin Coja‐Oghlan, Max Hahn‐Klimroth, Joon Lee, Noëla Müller, Manuel Penschuck, Guangyan Zhou   +6 more
wiley   +1 more source

Computing LF‐Metric Dimension of Generalized Gear Networks

Mathematical Problems in Engineering, Volume 2021, Issue 1, 2021., 2021
The parameter of distance in the theory of networks plays a key role to study the different structural properties of the understudy networks or graphs such as symmetry, assortative, connectivity, and clustering. For the purpose, with the help of the parameter of distance, various types of metric dimensions have been defined to find the locations of ...
Hassan Zafar, Muhammad Javaid, Ebenezer Bonyah, Muhammad Faisal Nadeem   +3 more
wiley   +1 more source

More on Spectral Analysis of Signed Networks

Complexity, Volume 2018, Issue 1, 2018., 2018
Spectral graph theory plays a key role in analyzing the structure of social (signed) networks. In this paper we continue to study some properties of (normalized) Laplacian matrix of signed networks. Sufficient and necessary conditions for the singularity of Laplacian matrix are given.
Guihai Yu, Hui Qu, Piotr Brodka
wiley   +1 more source

γ-Inverse graph of some mixed graphs

Special Matrices
Let GG be a graph. Then, the inverse graph G−1{G}^{-1} of GG is defined to be a graph that has adjacency matrix similar to the inverse of the adjacency matrix of GG, where the similarity matrix is ±1\pm 1 diagonal matrix. In this article, we introduced a
Boulahmar Wafa, Ghanem Manal, Abudayah Mohammad   +2 more
doaj   +1 more source

Extremal Bipartite Graphs and Unicyclic Graphs With Respect to the Eccentric Resistance-Distance Sum

Journal of Mathematical Analysis and Applications, 2021
Changlong Shen, Shuchao Li
exaly  

On Unicyclic Non-Bipartite Graphs With Tricyclic Inverses

Linear and Multilinear Algebra, 2023
Debajit Kalita
exaly  

On the Smallest Positive Eigenvalue of Bipartite Unicyclic Graphs With a Unique Perfect Matching

Discrete Mathematics, 2023
Sasmita Barik
exaly  

Inverses of Non-Bipartite Unicyclic Graphs With a Unique Perfect Matching

Linear and Multilinear Algebra, 2022
Debajit Kalita
exaly  

The Bipartite Unicyclic Graphs With the First ⌊n−34⌋ Largest Matching Energies

Applied Mathematics and Computation, 2015
Jinfeng Liu, Lin Chen
exaly