Results 71 to 80 of about 298 (175)
Journal of Mathematics, Volume 2025, Issue 1, 2025.The multiplicative sum Zagreb index of a graph G is defined as the product of the sum of the degrees of adjacent vertices of G. A molecular tree is an acyclic connected graph with maximum degree at most 4. A vertex in a molecular tree with degree 3 or 4 is referred to as a branching vertex. In this paper, we consider the class of all molecular trees of
Sadia Noureen +6 more
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Unicyclic graphs with maximal energy
Linear Algebra and its Applications, 2002 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hou, Yaoping +2 more
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Extremal Unicyclic Graphs With Minimal Distance Spectral Radius
Discussiones Mathematicae Graph Theory, 2014 The distance spectral radius ρ(G) of a graph G is the largest eigenvalue of the distance matrix D(G). Let U (n,m) be the class of unicyclic graphs of order n with given matching number m (m ≠ 3).
Lu Hongyan, Luo Jing, Zhu Zhongxun
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On the Maximum SC Index of Chemical Unicyclic Graphs
Journal of Mathematics, Volume 2025, Issue 1, 2025.The sum‐connectivity (SC) index of a graph G is defined as SCG=∑μν∈EG1/Θμ+Θν, where Θμ denotes the vertex degree of μ in G. In this paper, the fourth largest value of SC index for the chemical unicyclic graphs of order n ≥ 7 is determined.
Hui-Yan Cheng +3 more
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Mathematika, Volume 70, Issue 4, October 2024.Abstract Given a graph on n$n$ vertices with m$m$ edges, each of unit resistance, how small can the average resistance between pairs of vertices be? There are two very plausible extremal constructions — graphs like a star, and graphs which are close to regular — with the transition between them occurring when the average degree is 3.
J. Robert Johnson, Mark Walters
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A note on the width of sparse random graphs
Journal of Graph Theory, Volume 106, Issue 2, Page 273-295, June 2024.Abstract In this note, we consider the width of a supercritical random graph according to some commonly studied width measures. We give short, direct proofs of results of Lee, Lee and Oum, and of Perarnau and Serra, on the rank‐ and tree‐width of the random graph G(n,p) $G(n,p)$ when p=1+ϵn $p=\frac{1+\epsilon }{n}$ for ϵ>0 $\epsilon \gt 0$ constant ...
Tuan Anh Do, Joshua Erde, Mihyun Kang
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IET Control Theory &Applications, Volume 18, Issue 8, Page 977-986, May 2024.Abstract This paper is concerned with the synchronization of stochastic uncertain complex dynamic networks with time‐varying delays. In contrast to existing synchronization network models, the current study considers both internal time‐varying delays and coupling time‐varying delays. By analyzing the two factors (i.e.
Xuhui Guo +3 more
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Brooks' theorem with forbidden colors
Journal of Graph Theory, Volume 105, Issue 3, Page 373-385, March 2024.Abstract We consider extensions of Brooks' classic theorem on vertex coloring where some colors cannot be used on certain vertices. In particular we prove that if G $G$ is a connected graph with maximum degree Δ(G)≥4 ${\rm{\Delta }}(G)\ge 4$ that is not a complete graph and P⊆V(G) $P\subseteq V(G)$ is a set of vertices where either (i) at most Δ(G)−2 ${
Carl Johan Casselgren
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Journal of Mathematics, Volume 2024, Issue 1, 2024.Nanostar dendrimers are tree‐like nanostructures with a well‐defined, symmetrical architecture. They are built in a step‐by‐step, controlled synthesis process, with each layer or generation building on the previous one. Dendrimers are made up of a central core, a series of repeating units or branches, and a surface group shell.
Syed Ahtsham Ul Haq Bokhary +7 more
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Spectrum of Unicyclic Graph [PDF]
Advances in Computer Science Research, 2022 Agung Lukito +3 more
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