Results 171 to 180 of about 580,793 (206)

Spectra of unicyclic graphs

Graphs and Combinatorics, 1987
We study lexicographic ordering of unicyclic graphs by spectral moments as well as the ordering by the largest eigenvalue. If the length of the cycle is fixed, extremal graphs in the first ordering are obtained by attaching a star and a path to a cycle. For the other ordering minimal graphs are not known.
Peter Rowlinson, Dragos Cvetković
exaly   +3 more sources

On the multiplicity of Laplacian eigenvalues for unicyclic graphs [PDF]

Czechoslovak Mathematical Journal, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wen, Fei, Huang, Qiongxiang
openaire   +2 more sources

Largest eigenvalue of a unicyclic mixed graph

Applied Mathematics, 2004
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exaly   +3 more sources

The k-Metric Dimension of a Unicyclic Graph

Mathematics, 2021
Given a connected graph G=(V(G),E(G)), a set S & SUBE;V(G) is said to be a k-metric generator for G if any pair of different vertices in V(G) is distinguished by at least k elements of S.
Alejandro Estrada-Moreno
exaly   +1 more source

Unicyclic signed graphs with minimal energy

Discrete Applied Mathematics, 2017
A connected signed graph with n vertices is said to be unicyclic if its number of edges is n. The energy of a signed graph S of order n with eigenvalues x(1), x(2), ..., x(n) is defined as E(S)=Sigma(n)(j=1) |x(j)|. We obtain the integral representations
Shariefuddin Pirzada
exaly   +2 more sources

Integral unicyclic graphs

Linear Algebra and its Applications, 2021
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Rodrigo O. Braga, Renata R. Del-Vecchio, Virgínia M. Rodrigues   +2 more
openaire   +1 more source

On broadcasting in unicyclic graphs

Journal of Combinatorial Optimization, 2008
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Hovhannes A. Harutyunyan, Edward Maraachlian   +1 more
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THE GUTMAN INDEX OF UNICYCLIC GRAPHS

Discrete Mathematics, Algorithms and Applications, 2012
Let G be a connected graph with vertex set V(G). The Gutman index of G is defined as S(G) = ∑{u, v}⊆V(G) d(u)d(v)d(u, v), where d(u) is the degree of vertex u, and d(u, v) denotes the distance between u and v. In this paper, we characterize n-vertex unicyclic graphs with girth k, having minimal Gutman index.
openaire   +2 more sources

Degree Condition for Subdivisions of Unicyclic Graphs

Graphs and Combinatorics, 2008
The authors prove the following results: Let \(H\) be any graph of order \(n\) with \(k\) vertex disjoint pieces \(H_1,\dots, H_k\), each of which contains at most one cycle. Let \(G\) be any graph of order at least \(n\) with \(\delta (G) \geq n -k \). Then \(G\) contains a cyclic subdivision of \(H\).
BABU, C, DIWAN, A
openaire   +4 more sources

Trees and unicyclic graphs with hamiltonian path graphs

Journal of Graph Theory, 1990
AbstractWe prove two conjectures of Broersma and Hoede about path graphs of trees and unicyclic graphs.
openaire   +1 more source