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Characterization of the Minimizing Graph of the Connected Graphs Whose Complements Are Bicyclic [PDF]
Mathematics, 2017 In a certain class of graphs, a graph is called minimizing if the least eigenvalue of its adjacency matrix attains the minimum. A connected graph containing two or three cycles is called a bicyclic graph if its number of edges is equal to its number of ...
Muhammad Javaid, Javaid Muhammad
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Metric Dimensions of Bicyclic Graphs
Mathematics, 2023 The distance d(va,vb) between two vertices of a simple connected graph G is the length of the shortest path between va and vb. Vertices va,vb of G are considered to be resolved by a vertex v if d(va,v)≠d(vb,v).
Asad Khan +5 more
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The Maximal Total Irregularity of Bicyclic Graphs [PDF]
Journal of Applied Mathematics, 2014 In 2012, Abdo and Dimitrov defined the total irregularity of a graph G=(V,E) as irrtG=1/2∑u,v∈VdGu-dGv, where dGu denotes the vertex degree of a vertex u∈V.
Lihua You +3 more
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On the Signless Laplacian Spectral Radius of Bicyclic Graphs with Perfect Matchings [PDF]
The Scientific World Journal, 2014 The graph with the largest signless Laplacian spectral radius among all bicyclic graphs with perfect matchings is determined.
Jing-Ming Zhang +2 more
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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.
Yi-Zheng Fan
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On the Laplacian spectral radii of bicyclic graphs
Discrete Mathematics, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jia-Yu Shao
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On the harmonic index of bicyclic graphs
Communications in Combinatorics and Optimization, 2018 The harmonic index of a graph $G$, denoted by $H(G)$, is defined as the sum of weights $2/[d(u)+d(v)]$ over all edges $uv$ of $G$, where $d(u)$ denotes the degree of a vertex $u$. Hu and Zhou [Y. Hu and X. Zhou, WSEAS Trans. Math.
R. Rasi
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Bicyclic molecular graphs with the greatest energy [PDF]
Journal of the Serbian Chemical Society, 2008 The molecular graph Qn is obtained by attaching hexagons to the end vertices of the path graph Pn-12. Earlier empirical studies indicated that Qn has greatest energy among all bicyclic n-vertex (molecular) graphs.
IVAN GUTMAN +2 more
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CONSTRUCTION OF BICYCLIC GRAPH AND ITS APPLICATION IN TRANS JOGJA ROUTES
Barekeng, 2023 A bicyclic graph is a type of graph that consists of exactly two cycles. A cycle is a graph that is a closed path where no vertices are repeated except the first and last vertices which are the same.
Aditya Ambarwati, Vira Hari Krisnawati
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The Aα-spectral radius of complements of bicyclic and tricyclic graphs with n vertices
Special Matrices, 2021 Recently, the extremal problem of the spectral radius in the class of complements of trees, unicyclic graphs, bicyclic graphs and tricyclic graphs had been studied widely.
Chen Chaohui +2 more
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