Results 31 to 40 of about 1,962 (215)
The Orderings of Bicyclic Graphs and Connected Graphs by Algebraic Connectivity [PDF]
The Electronic Journal of Combinatorics, 2010 The algebraic connectivity of a graph $G$ is the second smallest eigenvalue of its Laplacian matrix. Let $\mathscr{B}_n$ be the set of all bicyclic graphs of order $n$. In this paper, we determine the last four bicyclic graphs (according to their smallest algebraic connectivities) among all graphs in $\mathscr{B}_n$ when $n\geq 13$.
Jianxi Li, Ji-Ming Guo, Wai Chee Shiu
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Maximum Reciprocal Degree Resistance Distance Index of Bicyclic Graphs
Discrete Dynamics in Nature and Society, 2021 The reciprocal degree resistance distance index of a connected graph G is defined as RDRG=∑u,v⊆VGdGu+dGv/rGu,v, where rGu,v is the resistance distance between vertices u and v in G. Let ℬn denote the set of bicyclic graphs without common edges and with n
Gaixiang Cai, Xing-Xing Li, Guidong Yu
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Applied Mathematics Letters, 2005 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Stefan Grünewald, Dragan Stevanovic
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Unbalanced unicyclic and bicyclic graphs with extremal spectral radius [PDF]
, 2021 summary:A signed graph $\Gamma $ is a graph whose edges are labeled by signs. If $\Gamma $ has $n$ vertices, its spectral radius is the number $\rho (\Gamma ) := \max \{ | \lambda _i(\Gamma ) | \colon 1 \leq i \leq n \}$, where $\lambda _1(\Gamma ) \geq \
Brunetti, Maurizio +2 more
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Further Results on the Nullity of Signed Graphs
Journal of Applied Mathematics, 2014 The nullity of a graph is the multiplicity of the eigenvalue zero in its spectrum. A signed graph is a graph with a sign attached to each of its edges. In this paper, we apply the coefficient theorem on the characteristic polynomial of a signed graph and
Yu Liu, Lihua You
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On Omega Index and Average Degree of Graphs
Journal of Mathematics, 2021 Average degree of a graph is defined to be a graph invariant equal to the arithmetic mean of all vertex degrees and has many applications, especially in determining the irregularity degrees of networks and social sciences.
Sadik Delen +3 more
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On the inverse mostar index problem for molecular graphs [PDF]
Transactions on CombinatoricsMostar indices are recently proposed distance-based graph invariants, that already have been much investigated and found applications. In this paper, we investigate the inverse problem for Mostar indices of unicyclic and bicyclic molecular graphs.
Liju Alex, Ivan Gutman
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ARITHMETICAL RANK OF THE CYCLIC AND BICYCLIC GRAPHS [PDF]
Journal of Algebra and Its Applications, 2012 We show that for the edge ideals of the graphs consisting of one cycle or two cycles of any length connected through a vertex, the arithmetical rank equals the projective dimension of the corresponding quotient ring.
BARILE, Margherita +3 more
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Mathematics, 2023 Degree sequence measurements on graphs have attracted a lot of research interest in recent decades. Multiplying the degrees of adjacent vertices in graph Ω provides the multiplicative first Zagreb index of a graph.
Sakander Hayat, Farwa Asmat
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Maximum Estrada index of bicyclic graphs
Discrete Applied Mathematics, 2015 Let $G$ be a simple graph of order $n$, let $λ_1(G),λ_2(G),...,λ_n(G)$ be the eigenvalues of the adjacency matrix of $G$. The Esrada index of $G$ is defined as $EE(G)=\sum_{i=1}^{n}e^{λ_i(G)}$. In this paper we determine the unique graph with maximum Estrada index among bicyclic graphs with fixed order.
Long Wang 0013, Yi-Zheng Fan, Yi Wang
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