Results 21 to 30 of about 4,390 (196)
Regularity of bicyclic graphs and their powers [PDF]
Journal of Algebra and Its Applications, 2019 Let [Formula: see text] be the edge ideal of a bicyclic graph [Formula: see text] with a dumbbell as the base graph. In this paper, we characterize the Castelnuovo–Mumford regularity of [Formula: see text] in terms of the induced matching number of [Formula: see text]. For the base case of this family of graphs, i.e.
Cid-Ruiz, Yairon +3 more
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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
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Applied Mathematics Letters, 2005 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Grünewald, Stefan, Stevanović, Dragan
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Maximal elliptic Sombor index of bicyclic graphs [PDF]
Contributions to MathematicsFuxian Qi, Zhen Lin
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The first Dirichlet eigenvalue of bicyclic graphs [PDF]
Czechoslovak Mathematical Journal, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhang, Guang-Jun, Zhang, Xiao-Dong
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Bicyclic graphs with maximum sum of the two largest Laplacian eigenvalues
Journal of Inequalities and Applications, 2016 Let G be a simple connected graph and S 2 ( G ) $S_{2}(G)$ be the sum of the two largest Laplacian eigenvalues of G. In this paper, we determine the bicyclic graph with maximum S 2 ( G ) $S_{2}(G)$ among all bicyclic graphs of order n, which confirms the
Yirong Zheng +3 more
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Discrete Mathematics, 2008 Let \(\lambda_2\) be the second largest eigenvalue of the adjacency matrix of a graph. Graphs having \(\lambda_2\leq 2\) are called reflexive graphs. Since this property is hereditary, these graphs may be represented through sets of maximal graphs. In this paper, authors continue their previous line of study and construct maximal bicyclic reflexive ...
Radosavljević, Zoran +2 more
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Non-Singular Trees, Unicyclic Graphs and Bicyclic Graphs
Applied Mathematics, 2020 We called graph G non-singular if adjacency matrix A (G) of G is non-singular. A connected graph with n vertices and n-1, n and n+1 edges are called the tree, the unicyclic graph and the bicyclic graph. Respectively, as we all know, each connected bicyclic graph must contain ∞(a,s,b) or θ(p,l,q) as the induced subgraph.
Haicheng Ma, Danyang Li, Chengling Xie
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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 $n\geq 13$.
Li, Jianxi, Guo, Ji-Ming, Shiu, Wai Chee
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On extremal bipartite bicyclic graphs
Journal of Mathematical Analysis and Applications, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Huang, Jing, Li, Shuchao, Zhao, Qin
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