Results 41 to 50 of about 2,448,104 (66)

Unicyclic graphs with strong reciprocal eigenvalue property

, 2008
A graph G is bipartite if and only if the negative of each eigenvalue of G is also an eigenvalue of G. It is said that a graph has property (R), if G is nonsingular and the reciprocal of each of its eigenvalues is also an eigenvalue.
Pati, Sukanta, Sarma, Bhaba, Nath, Milan, Sarma, Bhaba Kumar, Barik, Sasmita   +4 more
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Degree distance of unicyclic graphs

, 2010
The degree distance of a connected graph G with vertex set V(G) is defined as D'(G)= ?u?V (G) dG (u)DG (u), where dG (u) denotes the degree of vertex u and DG (u) denotes the sum of distances between u and all vertices of G.
Bo Zhou, Zhibin Du
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Locating eigenvalues of unicyclic graphs

, 2017
We present a linear time algorithm that computes the number of eigenvalues of a unicyclic graph in a given real interval. It operates directly on the graph, so that the matrix is not needed explicitly.
Virgínia Rodrigues, Vilmar Trevisan, Rodrigo Braga   +2 more
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Bounds for the geometric-arithmetic index of unicyclic graphs

, 2023
We present lower and upper bounds for the geometric-arithmetic index of unicyclic graphs and provide extremal graphs for the corresponding ...
Moon, Sunyo, Park, Seungkook
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Unicyclic signed graphs with minimal energy

, 2017
A connected signed graph with n vertices is said to be unicyclic if its number of edges is n. The energy of a signed graph S of order n with eigenvalues x(1), x(2), ..., x(n) is defined as E(S)=Sigma(n)(j=1) |x(j)|. We obtain the integral representations
S. Pirzada, Mushtaq A. Bhat, BHAT, MA, PIRZADA, S   +3 more
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On bipartite-mixed graphs

Mixed graphs can be seen as digraphs that have both arcs and edges (or digons, that is, two opposite arcs). In this paper, we consider the case where such graphs are bipartite.
Dalfó Simó, Cristina, Fiol Mora, Miquel Àngel, López Lorenzo, Nacho   +2 more
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Maximal energy bipartite graphs

, 2003
Given a graph $G$, its energy $E(G)$ is defined to be the sum of the absolute values of the eigenvalues of $G$. This quantity is used in chemistry to approximate the total $\pi$-electron energy of molecules and in particular, in case $G$ is bipartite ...
Moulton, Vincent, Koolen, Jack H., Moulton, Vincent,, Koolen, J H   +3 more
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Inverse of $\alpha$-Hermitian Adjacency Matrix of a Unicyclic Bipartite Graph

, 2022
Let $X$ be bipartite mixed graph and for a unit complex number $\alpha$, $H_\alpha$ be its $\alpha$-hermitian adjacency matrix. If $X$ has a unique perfect matching, then $H_\alpha$ has a hermitian inverse $H_\alpha^{-1}$.
Alomari, Omar, AbuGhneim, Omar, Abudayah, Mohammad   +2 more
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Spectral radius and extremal graphs for class of unicyclic graph with pendant vertices

, 2017
In this article, we research on the spectral radius of extremal graphs for the unicyclic graphs with girth g mainly by the graft transformation and matching and obtain the upper bounds of the spectral radius of unicyclic graphs.
Chen Chen, Yan-Jun Liu, Xiaodong Chen, Lu Zhi, Meijin Xu, Xiujuan Liu   +5 more
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Gracefulness of unicyclic graphs

, 2015
С использованием конструктивных и аналитических методов решается задача существования грациозной разметки для одноциклических графов. Доказана грациозность некоторых представителей этого класса графов.Із застосуванням конструктивних та аналітичних ...
Семенюта, М.Ф.
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