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The Nullity of Bicyclic Signed Graphs [PDF]
Linear and Multilinear Algebra, 2012 Let \Gamma be a signed graph and let A(\Gamma) be the adjacency matrix of \Gamma. The nullity of \Gamma is the multiplicity of eigenvalue zero in the spectrum of A(\Gamma).
Cheng B +7 more
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Further Results on the Nullity of Signed Graphs [PDF]
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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Bicyclic Graphs with the Second-Maximum and Third-Maximum Degree Resistance Distance [PDF]
Journal of Mathematics, 2021 Let G=V,E be a connected graph. The resistance distance between two vertices u and v in G, denoted by RGu,v, is the effective resistance between them if each edge of G is assumed to be a unit resistor.
Wenjie Ning, Kun Wang, Hassan Raza
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On the Hosoya Indices of Bicyclic Graphs with Small Diameter [PDF]
Journal of Chemistry, 2021 Let G be a graph. The Hosoya index of G, denoted by zG, is defined as the total number of its matchings. The computation of zG is NP-Complete. Wagner and Gutman pointed out that it is difficult to obtain results of the maximum Hosoya index among tree ...
Tingzeng Wu, Yong Yu
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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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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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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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On the Extremal Weighted Mostar Index of Bicyclic Graphs [PDF]
AxiomsLet G be a simple connected graph with edge set E(G) and vertex set V(G). The weighted Mostar index of a graph G is defined as w+Mo(G)=∑e=uv∈E(G)(dG(u)+dG(v))|nu(e)−nv(e)|, where nu(e) denotes the number of vertices closer to u than to v for an edge uv ...
Yuwei He, Mengmeng Liu
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On Extended Adjacency Index with Respect to Acyclic, Unicyclic and Bicyclic Graphs [PDF]
Mathematics, 2019 For a (molecular) graph G, the extended adjacency index E A ( G ) is defined as Equation (1). In this paper we introduce some graph transformations which increase or decrease the extended adjacency ( E A ) index.
Bin Yang +4 more
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LOCAL IRREGULARITY VERTEX COLORING OF BICYCLIC GRAPH FAMILIES
BarekengThe graph in this research is a simple and connected graph with as vertex set and as an edge set. We used deductive axiomatic and pattern recognition method.
Arika Indah Kristiana +5 more
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