Results 111 to 120 of about 828 (207)

Locating eigenvalues of unicyclic graphs

, 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.
Virgínia Rodrigues, Vilmar Trevisan, Rodrigo Braga   +2 more
core   +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

Spectrum of Unicyclic Graph [PDF]

Advances in Computer Science Research, 2022
Agung Lukito, Raden Sulaiman, Dwi Nur Yunianti, Budi Rahadjeng   +3 more
openaire   +1 more source

Resistance matrix and q-Laplacian of a unicyclic graph

, 2008
: The resistance distance between two vertices of a graph can be defined as the effective resistance between the two vertices, when the graph is viewed as an electrical network with each edge carrying unit resistance.
R. B. Bapat
core  

Some results on the Laplacian eigenvalues of unicyclic graphs

, 2009
In this paper, we provide the smallest value of the second largest Laplacian eigenvalue for any unicyclic graph, and find the unicyclic graphs attaining that value.
Li, Jianxi, Chan, Wai Hong, Shiu, Wai Chee   +2 more
core   +1 more source

Solutions of Detour Distance Graph Equations. [PDF]

Sensors (Basel), 2022
Prabha SC, Palanivel M, Amutha S, Anbazhagan N, Cho W, Song HK, Joshi GP, Moon H.   +7 more
europepmc   +1 more source

Unicyclic graphs with maximal energy

, 2002
Let G be a graph on n vertices and let λ1,λ2,…,λn be its eigenvalues. The energy of G is defined as E(G)=|λ1|+|λ2|+⋯+|λn|. For various classes of unicyclic graphs, the graphs with maximal energy are determined.
Woo, Ching-Wah, Hou, Yaoping, Gutman, Ivan   +2 more
core   +1 more source

The determinant of a unicyclic graph’s neighborhood matrix

Linear Algebra and its Applications, 2005
Let \(G\) be a unicyclic graph with \(n\) vertices and a unique cycle, \(A(G)\) denotes the adjacency matrix of the graph \(G\). The algorithm for computing the determinant function of the matrix \(\alpha I_n+A(G)\) which uses \(O(n)\) arithmetic operations under some restrictions on the degrees of the vertices of the graph \(G\) is obtained. Among the
openaire   +2 more sources

Degree distance of unicyclic graphs

, 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.
Bo Zhou, Zhibin Du
core   +1 more source

On the Laplacian index of tadpole graphs

Special Matrices
In this article, we study the Laplacian index of tadpole graphs, which are unicyclic graphs formed by adding an edge between a cycle Ck{C}_{k} and a path Pn{P}_{n}.
Braga Rodrigo O., Veloso Bruno S.
doaj   +1 more source