Results 181 to 190 of about 580,793 (206)

Unicyclic Graphs with Minimal Energy

Journal of Mathematical Chemistry, 2001
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Trees and Unicyclic Graphs

The Mathematics Teacher, 1967
There are many results in mathematics that are both new and elementary. Graph theory, which abounds in theorems of this kind, is the source of an interesting self-contained example which we present in this article.
Sabra S. Anderson, Frank Harary
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Cycles and Unicyclic Components in Random Graphs

Combinatorics, Probability and Computing, 2003
Let \(G(n,m)\) denote a graph selected uniformly and at random from all graphs on \(n\) labelled vertices with \(m=m(n)\) edges. We say \(G(n,m)\) has a property \(\wp\) whp if \[ \lim_{n\rightarrow\infty}P\{G(n,m)\text{ has }\wp\}=1. \] Throughout the article under review, \(m=n/2\pm s\) where \(n^{2/3}=o(s)\) and \(s=o(n)\).
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On the degree Kirchhoff index of unicyclic graphs

Discrete Applied Mathematics, 2020
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Xuli Qi, Bo Zhou 0007
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On the Laplacian coefficients of unicyclic graphs with prescribed matching number [PDF]

Discrete Mathematics, 2011
Let ϕ(G,λ)=∑k=0n(−1)kck(G)λn−k be the characteristic polynomial of the Laplacian matrix of a graph G of order n. We give some transformations of connected graphs that decrease all Laplacian coefficients ck(G), we then derive the unicyclic graphs with the
Tan, Shang-wang, Shang-wang Tan
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On the minimal matching energies of unicyclic graphs

Discrete Applied Mathematics, 2019
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Jianming Zhu, Ju Yang
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Algorithms for optimal orientations of a unicyclic graph

Proceedings of the 42nd annual Southeast regional conference, 2004
Let (G, R) denote the directed graph obtained from undirected graph G by an acyclic orientation R so that (G, R) contains no directed cycle. We consider acyclic orientations R of a unicyclic graph G which maximizes/minimizes the number of ordered pairs of non-adjacent vertices with directed paths in (G, R).
Suk Jai Seo, Ashok T. Amin
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Unicyclic graphs with regular endomorphism monoids

Discrete Mathematics, Algorithms and Applications, 2016
The motivation of this paper comes from an open question: which graphs have regular endomorphism monoids? In this paper, we give a definitely answer for unicyclic graphs, proving that a unicyclic graph [Formula: see text] is End-regular if and only if, either [Formula: see text] is an even cycle with 4, 6 or 8 vertices, or [Formula: see text] contains ...
Xiaobin Ma, Dein Wong, Jinming Zhou
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Dot product dimension of unicyclic graphs

Discrete Applied Mathematics
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Mahin Bahrami, Dariush Kiani, Asghar Bahmani   +2 more
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On Sombor Index of Unicyclic and Bicyclic Graphs

Journal of Interconnection Networks
Gutman proposed a topological index called the Sombor index, which was defined as [Formula: see text] where [Formula: see text] is the degree of the vertex [Formula: see text] in graph [Formula: see text]. In this paper, we determine the second-minimum and second-maximum values of the Sombor index over all the unicyclic graphs of order [Formula: see ...
Huan Tan, Biao Zhao
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