Results 31 to 40 of about 4,390 (196)
Unicyclic graphs with bicyclic inverses [PDF]
Czechoslovak Mathematical Journal, 2017 A graph is nonsingular if its adjacency matrix A(G) is nonsingular. The inverse of a nonsingular graph G is a graph whose adjacency matrix is similar to A(G)−1 via a particular type of similarity. Let H denote the class of connected bipartite graphs with unique perfect matchings.
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End-regularity of generalized bicycle graph
AKCE International Journal of Graphs and Combinatorics, 2020 A graph G is called End-regular, if every endomorphism of G is regular as a monoid. In this article, we investigate End-regularity of bicycle graphs. Moreover, a generalization of bicycle graph is defined and gives a characterization of End-regular generalized bicycle graphs.
A. Rajabi, A. Erfanian, A. Azimi
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Signed bicyclic graphs with minimal index
, 2022 Summary: The index \(\lambda_1(\Gamma)\) of a signed graph \(\Gamma=(G,\sigma)\) is just the largest eigenvalue of its adjacency matrix. For any \(n \geqslant 4\) we identify the signed graphs achieving the minimum index in the class of signed bicyclic graphs with \(n\) vertices.
Brunetti M., Ciampella A.
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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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Zagreb Indices of Trees, Unicyclic and Bicyclic Graphs With Given (Total) Domination
IEEE Access, 2019 Let G = (V, E) be a (molecular) graph. For a family of graphs G, the first Zagreb index M1 and the second Zagreb index M2 have already studied. In particular, it has been presented, the first Zagreb index M1 and the second Zagreb index M2 of trees T in ...
Doost Ali Mojdeh +3 more
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On the maximum Graovac-Pisanski index of bicyclic graphs
AIMS Mathematics, 2023 For a simple graph $ G = (V(G), E(G)) $, the Graovac-Pisanski index of $ G $ is defined as $ GP(G) = \frac{|V(G)|}{2|{\rm{Aut}}(G)|}\sum\limits_{u\in V(G)}\sum\limits_{\alpha\in {\rm{Aut}}(G)}d_G(u,\alpha(u)), $ where $ {\rm{Aut}}(G) $ is the ...
Jian Lu , Zhongxiang Wang
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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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Vertex-colored graphs, bicycle spaces and Mahler measure [PDF]
Journal of Knot Theory and Its Ramifications, 2016 The space [Formula: see text] of conservative vertex colorings (over a field [Formula: see text]) of a countable, locally finite graph [Formula: see text] is introduced. When [Formula: see text] is connected, the subspace [Formula: see text] of based colorings is shown to be isomorphic to the bicycle space of the graph.
Lamey, Kalyn R. +2 more
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On minimum revised edge Szeged index of bicyclic graphs
AKCE International Journal of Graphs and Combinatorics, 2022 The revised edge Szeged index [Formula: see text] of a graph G is defined as [Formula: see text] where [Formula: see text] and [Formula: see text] are, respectively, the number of edges of G lying closer to vertex u than to vertex v and the number of ...
Mengmeng Liu, Shengjin Ji
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Maximizing spectral radii of uniform hypergraphs with few edges
, 2015 In this paper we investigate the hypergraphs whose spectral radii attain the maximum among all uniform hypergraphs with given number of edges. In particular we characterize the hypergraph(s) with maximum spectral radius over all unicyclic hypergraphs ...
Fan, Yi-Zheng +3 more
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