Results 21 to 30 of about 828 (207)

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
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Extremal Values on the General Degree–Eccentricity Index of Unicyclic Graphs of Fixed Diameter

Journal of Mathematics
For a connected graph G and two real numbers a,b, the general degree–eccentricity index of G is given by DEIa,bG=∑v∈VGdGavecGbv, where VG represent the vertex set of graph G, dGv denotes the degree of vertex v, and ecGv is the eccentricity of v in G ...
Mesfin Masre
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Online graph exploration on trees, unicyclic graphs and cactus graphs [PDF]

Information Processing Letters, 2021
We study the problem of exploring all vertices of an undirected weighted graph that is initially unknown to the searcher. An edge of the graph is only revealed when the searcher visits one of its endpoints. Beginning at some start node, the searcher's goal is to visit every vertex of the graph before returning to the start node on a tour as short as ...
Fritsch, Robin
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On the least signless Laplacian eigenvalue of a non-bipartite connected graph with fixed maximum degree [PDF]

Journal of Inequalities and Applications, 2017
In this paper, we determine the unique graph whose least signless Laplacian eigenvalue attains the minimum among all non-bipartite unicyclic graphs of order n with maximum degree Δ and among all non-bipartite connected graphs of order n with maximum ...
Shu-Guang Guo, Rong Zhang
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Some Results on the Independence Polynomial of Unicyclic Graphs

Discussiones Mathematicae Graph Theory, 2018
Let G be a simple graph on n vertices. An independent set in a graph is a set of pairwise non-adjacent vertices. The independence polynomial of G is the polynomial I(G,x)=∑k=0ns(G,k)xk$I(G,x) = \sum\nolimits_{k = 0}^n {s\left({G,k} \right)x^k }$, where s(
Oboudi Mohammad Reza
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On Unicyclic Graphs Spectra: New Results

2016 IEEE Intl Conference on Computational Science and Engineering (CSE) and IEEE Intl Conference on Embedded and Ubiquitous Computing (EUC) and 15th Intl Symposium on Distributed Computing and Applications for Business Engineering (DCABES), 2016
Let G = (V, E) be a unicyclic simple undirected graph. In this paper, we investigate the spectra of a particular class of unicyclic graphs G(q, n1) where q is the size of the unique cycle. Each vertex of the unique cycle is attached to n1 vertices. We provide the " exact values " of the extremal eigenvalues of the adjacency matrix A and the Laplacian ...
Hadji, Makhlouf, Chau, Ming
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Laplacian Spectral Characterization of Some Unicyclic Graphs [PDF]

Journal of Applied Mathematics, 2014
Let W(n;q,m1,m2) be the unicyclic graph with n vertices obtained by attaching two paths of lengths m1 and m2 at two adjacent vertices of cycle Cq. Let U(n;q,m1,m2,…,ms) be the unicyclic graph with n vertices obtained by attaching s paths of lengths m1,m2,
Lijun Yu, Hui Wang, Jiang Zhou
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The number of independent sets in unicyclic graphs [PDF]

Discrete Applied Mathematics, 2005
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Pedersen, Anders Sune, Dahl Vestergaard, Preben   +1 more
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Resolving an Open Problem on the Exponential Arithmetic–Geometric Index of Unicyclic Graphs

Mathematics
Recently, the exponential arithmetic–geometric index (EAG) was introduced. The exponential arithmetic–geometric index (EAG) of a graph G is defined as EAG(G)=∑vivj∈E(G)edi+dj2didj, where di represents the degree of the vertex vi in G.
Kinkar Chandra Das, Jayanta Bera
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Decomposition of complete graphs into connected bipartite unicyclic graphs with eight edges

Electronic Journal of Graph Theory and Applications, 2019
We prove that each of the 34 non-isomorphic connected unicyclic bipartite graphs with eight edges decomposes the complete graph Kn whenever the necesary conditions are satisfied.
John Fahnenstiel, Dalibor Froncek
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