Results 41 to 50 of about 3,013 (185)

The Laplacian Spectral Radius of a Class of Unicyclic Graphs

Journal of Applied Mathematics, 2013
Let C(n,k) be the set of all unicyclic graphs with n vertices and cycle length k. For any U∈C(n,k), U consists of the (unique) cycle (say Ck) of length k and a certain number of trees attached to the vertices of Ck having (in total) n-k edges.
Haixia Zhang
doaj   +1 more source

Ordering graphs with large eccentricity-based topological indices

Journal of Inequalities and Applications, 2021
For a connected graph, the first Zagreb eccentricity index ξ 1 $\xi _{1}$ is defined as the sum of the squares of the eccentricities of all vertices, and the second Zagreb eccentricity index ξ 2 $\xi _{2}$ is defined as the sum of the products of the ...
Yunfang Tang, Xuli Qi
doaj   +1 more source

Locating Eigenvalues of a Symmetric Matrix whose Graph is Unicyclic

Trends in Computational and Applied Mathematics, 2021
We present a linear-time algorithm that computes in a given real interval the number of eigenvalues of any symmetric matrix whose underlying graph is unicyclic.
R. O. Braga, V. M. Rodrigues, R. O. Silva   +2 more
doaj   +1 more source

On the Laplacian Coefficients and Laplacian-Like Energy of Unicyclic Graphs with n Vertices and m Pendent Vertices

Journal of Applied Mathematics, 2012
Let Φ(G,λ)=det(λIn-L(G))=∑k=0n(-1)kck(G)λn-k be the characteristic polynomial of the Laplacian matrix of a graph G of order n. In this paper, we give four transforms on graphs that decrease all Laplacian coefficients ck(G) and investigate a conjecture A.
Xinying Pai, Sanyang Liu
doaj   +1 more source

Problems on Matchings and Independent Sets of a Graph

, 2018
Let $G$ be a finite simple graph. For $X \subset V(G)$, the difference of $X$, $d(X) := |X| - |N (X)|$ where $N(X)$ is the neighborhood of $X$ and $\max \, \{d(X):X\subset V(G)\}$ is called the critical difference of $G$. $X$ is called a critical set if $
Bhattacharya, Amitava, Mondal, Anupam, Murthy, T. Srinivasa   +2 more
core   +1 more source

Fast Construction on a Restricted Budget

Random Structures &Algorithms, Volume 67, Issue 4, December 2025.
ABSTRACT We introduce a model of a controlled random graph process. In this model, the edges of the complete graph Kn$$ {K}_n $$ are ordered randomly and then revealed, one by one, to a player called Builder. He must decide, immediately and irrevocably, whether to purchase each observed edge.
Alan Frieze, Michael Krivelevich, Peleg Michaeli   +2 more
wiley   +1 more source

The Largest Laplacian Spectral Radius of Unicyclic Graphs with Fixed Diameter

Journal of Applied Mathematics, 2013
We identify graphs with the maximal Laplacian spectral radius among all unicyclic graphs with n vertices and diameter d.
Haixia Zhang
doaj   +1 more source

Zagreb Indices of Trees, Unicyclic and Bicyclic Graphs With Given (Total) Domination

IEEE Access, 2019
Let G = (V, E) be a (molecular) graph. For a family of graphs G, the first Zagreb index M1 and the second Zagreb index M2 have already studied. In particular, it has been presented, the first Zagreb index M1 and the second Zagreb index M2 of trees T in ...
Doost Ali Mojdeh, Mohammad Habibi, Leila Badakhshian, Yongsheng Rao   +3 more
doaj   +1 more source

Eccentric connectivity index [PDF]

, 2010
The eccentric connectivity index $\xi^c$ is a novel distance--based molecular structure descriptor that was recently used for mathematical modeling of biological activities of diverse nature. It is defined as $\xi^c (G) = \sum_{v \in V (G)} deg (v) \cdot
Ilić, Aleksandar
core  

Revolutionaries and spies on trees and unicyclic graphs

, 2011
A team of $r$ {\it revolutionaries} and a team of $s$ {\it spies} play a game on a graph $G$. Initially, revolutionaries and then spies take positions at vertices.
Cranston, Daniel W., Smyth, Clifford D., West, Douglas B.   +2 more
core   +2 more sources