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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 +2 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 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 Laplacian coefficients of bicyclic graphs
Discrete Mathematics, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Haiying Shan
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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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Degree distance of unicyclic and bicyclic graphs
Discrete Applied Mathematics, 2011 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Aleksandar Ilić +2 more
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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.
Shuchao Li
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Computing the Determinant of the Distance Matrix of a Bicyclic Graph
Electronic Notes in Theoretical Computer Science, 2019 Abstract Let G be a connected graph with vertex set V = {v1, ..., vn}. The distance d(vi, vj) between two vertices vi and vj is the number of edges of a shortest path linking them. The distance matrix of G is the n × n matrix such that its (i, j)-entry is equal to d(vi, vj).
Ezequiel Dratman +2 more
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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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