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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 +3 more
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On the Maximum Sombor Index of Unicyclic Graphs with a Fixed Girth
Journal of Mathematics, 2022 Let G be a graph having the set of edges EG. Represent by dGu the degree of a vertex u of G. The Sombor (SO) index of G is defined as SOG=∑uv∈EGdGu2+dGv2. The length of a shortest cycle in a graph G is known as the girth of G.
B. Senthilkumar +5 more
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On symmetric division deg index of unicyclic graphs and bicyclic graphs with given matching number
AIMS Mathematics, 2021 Nowadays, it is an important task to find extremal values on any molecular descriptor with respect to different graph parameters. In a molecular graph, the vertices represent the atoms and the edges represent the chemical bonds in the terms of graph ...
Xiaoling Sun, Yubin Gao, Jianwei Du
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, 2021 A directed unicyclic graph is a directed graph that has only one directed cycle subgraph. A directed unicyclic helm graph Hn→ is obtained from a directed wheel graph Wn→ by adjoining a directed pendant edge at each vertex of the cycle.
Rizky P. Okfradifa, S. Aminah, K. Sugeng
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Gallai-Edmonds decomposition of unicyclic graphs from null space [PDF]
The American Journal of Combinatorics, 2022 In this paper, we compute the Gallai-Edmonds decomposition of a unicyclic graph $G$ using linear algebraic tools. More precisely, the Gallai-Edmonds decomposition of $G$ is obtained from the null space associated with adjacency matrices of its subtrees.
Luiz Emilio Allem +3 more
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Generating graceful unicyclic graphs from a given forest
AKCE International Journal of Graphs and Combinatorics, 2020 Acharya (1982) proved that every connected graph can be embedded in a graceful graph. The generalization of this result that, any set of graphs can be packed into a graceful graph was proved by Sethuraman and Elumalai (2005). Recently, Sethuraman et al. (
G. Sethuraman, V. Murugan
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New Diagonal Graph Ramsey Numbers of Unicyclic Graphs
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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Binomial edge ideals of unicyclic graphs [PDF]
International Journal of Algebra and Computation, 2021 Let [Formula: see text] be a connected graph on the vertex set [Formula: see text]. Then [Formula: see text]. In this paper, we prove that if [Formula: see text] is a unicyclic graph, then the depth of [Formula: see text] is bounded below by [Formula: see text]. Also, we characterize [Formula: see text] with [Formula: see text] and [Formula: see text].
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Regular Turán numbers and some Gan–Loh–Sudakov‐type problems
Journal of Graph Theory, Volume 102, Issue 1, Page 67-85, January 2023., 2023 Abstract Motivated by a Gan–Loh–Sudakov‐type problem, we introduce the regular Turán numbers, a natural variation on the classical Turán numbers where we restrict ourselves to the class of regular graphs. Among other results, we prove a striking supersaturation version of Mantel's theorem in the case of a regular host graph of odd order.
Stijn Cambie +2 more
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Ordering non-bipartite unicyclic graphs with pendant vertices by the least Q-eigenvalue
Journal of Inequalities and Applications, 2016 A unicyclic graph is a connected graph whose number of edges is equal to the number of vertices. Fan et al. (Discrete Math. 313:903-909, 2013) and Liu et al. (Electron. J.
Shu-Guang Guo +3 more
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