Results 11 to 20 of about 580,793 (206)

New Diagonal Graph Ramsey Numbers of Unicyclic Graphs [PDF]

Theory and Applications of Graphs, 2023
Grossman conjectured that R(G, G) = 2 · |V (G)| − 1, for all simple connected unicyclic graphs G of odd girth and |V (G)| ≥ 4. In this note, we prove his conjecture for various classes of G containing a triangle.
Richard M. Low, Ardak Kapbasov
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Unicyclic Graphs with the Fourth Extremal Wiener Indices

Journal of Chemistry, 2020
A graph is called unicyclic if the graph contains exactly one cycle. Unicyclic graphs with the fourth extremal Wiener indices are characterized. It is shown that, among all unicyclic graphs with n≥8 vertices, C5Sn−4 and C2u1,u2S3,Sn−4 attain the fourth ...
Guangfu Wang, Yujun Yang, Yuliang Cao, Shoujun Xu   +3 more
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Further Results on the Resistance-Harary Index of Unicyclic Graphs

Mathematics, 2019
The Resistance-Harary index of a connected graph G is defined as R H ( G ) = ∑ { u , v } ⊆ V ( G ) 1 r ( u , v ) , where r ( u , v ) is the resistance distance between vertices u and v in G.
Jian Lu, Shu-Bo Chen, Jia-Bao Liu, Xiang-Feng Pan, Ying-Jie Ji   +4 more
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The Extremal Unicyclic Graphs With Given Girth for Exponential VDB Topological Indices

Journal of Mathematics
Topological indices are widely used molecular structure descriptors in chemistry and pharmaceutics, which help analyze and predict the physicochemical properties and biological activity of compounds.
Zhenhua Su, Zikai Tang
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Restrained domination in unicyclic graphs [PDF]

Discussiones Mathematicae Graph Theory, 2009
Let G = (V,E) be a graph. A set S ⊆ V is a restrained dominating set if every vertex in V − S is adjacent to a vertex in S and to a vertex in V − S. The restrained domination number of G, denoted by γr(G), is the minimum cardinality of a restrained dominating set of G. A unicyclic graph is a connected graph that contains precisely one cycle.
Johannes H. Hattingh, Ernst J. Joubert, Marc Loizeaux, Andrew R. Plummer, Lucas C. van der Merwe   +4 more
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The Second Maximum Mostar Index of Unicyclic Graphs With Given Diameter

Journal of Mathematics
Topological invariants are key tools for studying the physicochemical and thermodynamic properties of chemical compounds. Recently, a new bond-additive distance-based graph invariant called the Mostar index has been developed.
Muhammad Amer Qureshi, Asad Ullah, Parvez Ali, Emad E. Mahmoud, Melaku Berhe Belay   +4 more
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On the nullity of unicyclic graphs [PDF]

Linear Algebra and its Applications, 2005
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xuezhong, Tan, Liu, Bolian
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On Critical Unicyclic Graphs with Cutwidth Four

AppliedMath, 2022
The cutwidth minimization problem consists of finding an arrangement of the vertices of a graph G on a line Pn with n=|V(G)| vertices in such a way that the maximum number of overlapping edges (i.e., the congestion) is minimized.
Zhenkun Zhang, Hongjian Lai
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Extremal Unicyclic Graphs With Minimal Distance Spectral Radius [PDF]

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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Extremal Values on the General Degree–Eccentricity Index of Unicyclic Graphs of Fixed Diameter

Journal of Mathematics
For a connected graph G and two real numbers a,b, the general degree–eccentricity index of G is given by DEIa,bG=∑v∈VGdGavecGbv, where VG represent the vertex set of graph G, dGv denotes the degree of vertex v, and ecGv is the eccentricity of v in G ...
Mesfin Masre
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