Results 81 to 90 of about 2,717 (193)

Unicyclic graphs with bicyclic inverses [PDF]

Czechoslovak Mathematical Journal, 2017
A graph is nonsingular if its adjacency matrix A(G) is nonsingular. The inverse of a nonsingular graph G is a graph whose adjacency matrix is similar to A(G)−1 via a particular type of similarity. Let H denote the class of connected bipartite graphs with unique perfect matchings.
openaire   +1 more source

A note on the width of sparse random graphs

Journal of Graph Theory, Volume 106, Issue 2, Page 273-295, June 2024.
Abstract In this note, we consider the width of a supercritical random graph according to some commonly studied width measures. We give short, direct proofs of results of Lee, Lee and Oum, and of Perarnau and Serra, on the rank‐ and tree‐width of the random graph G(n,p) $G(n,p)$ when p=1+ϵn $p=\frac{1+\epsilon }{n}$ for ϵ>0 $\epsilon \gt 0$ constant ...
Tuan Anh Do, Joshua Erde, Mihyun Kang
wiley   +1 more source

A note on the minimum reduced reciprocal Randic index of n-vertex unicyclic graphs

Kuwait Journal of Science, 2017
Recent studies show that the reduced reciprocal Randi? (RRR) index possesses the second-best correlating ability amongthe several well known topological indices.
Akbar Ali, Akhlaq A. Bhatti
doaj  

The Least Algebraic Connectivity of Graphs

Discrete Dynamics in Nature and Society, 2015
The algebraic connectivity of a graph is defined as the second smallest eigenvalue of the Laplacian matrix of the graph, which is a parameter to measure how well a graph is connected.
Guisheng Jiang, Guidong Yu, Jinde Cao
doaj   +1 more source

Graph theory‐based synchronization for stochastic uncertain complex dynamical networks via inverse optimal adaptive control

IET Control Theory &Applications, Volume 18, Issue 8, Page 977-986, May 2024.
Abstract This paper is concerned with the synchronization of stochastic uncertain complex dynamic networks with time‐varying delays. In contrast to existing synchronization network models, the current study considers both internal time‐varying delays and coupling time‐varying delays. By analyzing the two factors (i.e.
Xuhui Guo, Zhiyi Yao, Di Wang, Huaizhu Wang   +3 more
wiley   +1 more source

Brooks' theorem with forbidden colors

Journal of Graph Theory, Volume 105, Issue 3, Page 373-385, March 2024.
Abstract We consider extensions of Brooks' classic theorem on vertex coloring where some colors cannot be used on certain vertices. In particular we prove that if G $G$ is a connected graph with maximum degree Δ(G)≥4 ${\rm{\Delta }}(G)\ge 4$ that is not a complete graph and P⊆V(G) $P\subseteq V(G)$ is a set of vertices where either (i) at most Δ(G)−2 ${
Carl Johan Casselgren
wiley   +1 more source

Computation of Wiener and Wiener Polarity Indices of a Class of Nanostar Dendrimer Using Vertex Weighted Graphs

Journal of Mathematics, Volume 2024, Issue 1, 2024.
Nanostar dendrimers are tree‐like nanostructures with a well‐defined, symmetrical architecture. They are built in a step‐by‐step, controlled synthesis process, with each layer or generation building on the previous one. Dendrimers are made up of a central core, a series of repeating units or branches, and a surface group shell.
Syed Ahtsham Ul Haq Bokhary, Pakeeza Bashir, Allah Nawaz, Shreefa O. Hilali, Mohammed Alhagyan, Ameni Gargouri, Mohammed M. A. Almazah, Ram Jiwari   +7 more
wiley   +1 more source

Eigenspaces for \(-2\) in signed line graphs

The American Journal of Combinatorics
It is known that \(-2\) appears in the spectrum of a connected signed line graph if and only if its root is either (a) a balanced signed graph, not a tree, that spans a switching of the complete signed graph or (b) an unbalanced simply signed graph ...
Zoran Stanić
doaj   +1 more source

Induced Geodetic Sequence of a Graph [PDF]

Transactions on Combinatorics
A vertex subset $S$ of a graph $G=(V,E)$ is said to be a geodetic set if every vertex in $G$ is in some $u-v$ geodesic for any $u,v \in S$. The minimum cardinality of such a set is the geodetic number, which is denoted as $g(G)$.
Liju Olickal, John Mulloor
doaj   +1 more source

On the Minimum Variable Connectivity Index of Unicyclic Graphs with a Given Order

Discrete Dynamics in Nature and Society, 2020
The variable connectivity index, introduced by the chemist Milan Randić in the first quarter of 1990s, for a graph G is defined as ∑vw∈EGdv+γdw+γ−1/2, where γ is a non-negative real number and dw is the degree of a vertex w in G.
Shamaila Yousaf, Akhlaq Ahmad Bhatti, Akbar Ali   +2 more
doaj   +1 more source