Results 81 to 90 of about 3,013 (185)

On degree-based graph invariants of fixed-order unicyclic graphs with prescribed maximum degree

AIMS Mathematics
Consider a graph $ G $ having edge set $ E $, and denote by $ d_x $ the degree of a vertex $ x $ in $ G $. A unicyclic graph is defined as a connected graph containing exactly one cycle. This work focuses on unicyclic graphs of a fixed order and examines
Akbar Ali, Fehaid Salem Alshammari, Abdulaziz M. Alanazi, Taher S. Hassan   +3 more
doaj   +1 more source

Extremal Unicyclic Graphs With Minimal Distance Spectral Radius

Discussiones Mathematicae Graph Theory, 2014
The distance spectral radius ρ(G) of a graph G is the largest eigenvalue of the distance matrix D(G). Let U (n,m) be the class of unicyclic graphs of order n with given matching number m (m ≠ 3).
Lu Hongyan, Luo Jing, Zhu Zhongxun
doaj   +1 more source

Third Smallest Wiener Polarity Index of Unicyclic Graphs

Frontiers in Physics, 2020
The Wiener polarity index WP(G) of a graph G is the number of unordered pairs of vertices {u,v} where the distance between u and v is 3. In this paper, we determine the third smallest Wiener polarity index of unicyclic graphs. Moreover, the corresponding
Wei Fang, Wei Fang, Muhan Ma, FuYuan Chen, FuYuan Chen, Hufeng Dong   +5 more
doaj   +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

Degree distance of unicyclic graphs

Filomat, 2010
The degree distance of a connected graph G with vertex set V(G) is defined as D'(G)= ?u?V (G) dG (u)DG (u), where dG (u) denotes the degree of vertex u and DG (u) denotes the sum of distances between u and all vertices of G. We determine the maximum degree distance of n-vertex unicyclic graphs with given maximum degree, and the first seven maximum ...
Zhibin Du, Bo Zhou
openaire   +2 more sources

The Neighbor-Locating-Chromatic Number of Pseudotrees

, 2020
A $k$-coloring of a graph $G$ is a partition of the set of vertices of $G$ into $k$ independent sets, which are called colors. A $k$-coloring is neighbor-locating if any two vertices belonging to the same color can be distinguished from each other by the
Alcon, Liliana, Gutierrez, Marisa, Hernando, Carmen, Mora, Mercè, Pelayo, Ignacio M.   +4 more
core  

Locating eigenvalues of unicyclic graphs

Applicable Analysis and Discrete Mathematics, 2017
We present a linear time algorithm that computes the number of eigenvalues of a unicyclic graph in a given real interval. It operates directly on the graph, so that the matrix is not needed explicitly. The algorithm is applied to study the multiplicities of eigenvalues of closed caterpillars, obtain the spectrum of balanced closed ...
Braga, Rodrigo O., Rodrigues, Virginia M., Trevisan, Vilmar   +2 more
openaire   +2 more sources

Extremal unicyclic and bicyclic graphs of the Euler Sombor index

AIMS Mathematics
Topological indices are widely used to analyze and predict the physicochemical properties of compounds, and have good application prospects. Recently, the Euler Sombor index was introduced, which is defined as \begin{document}$ \begin{align} EP(G ...
Zhenhua Su, Zikai Tang
doaj   +1 more source

Restrained domination in unicyclic graphs

Discussiones Mathematicae Graph Theory, 2009
Let G = (V,E) be a graph. A set S ⊆ V is a restrained dominating set if every vertex in V − S is adjacent to a vertex in S and to a vertex in V − S. The restrained domination number of G, denoted by γr(G), is the minimum cardinality of a restrained dominating set of G. A unicyclic graph is a connected graph that contains precisely one cycle.
Johannes H. Hattingh, Ernst J. Joubert, Marc Loizeaux, Andrew R. Plummer, Lucas C. van der Merwe   +4 more
openaire   +1 more source