Results 11 to 20 of about 305 (179)
The Extremal Unicyclic Graphs With Given Girth for Exponential VDB Topological Indices
Journal of MathematicsTopological 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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The Second Maximum Mostar Index of Unicyclic Graphs With Given Diameter
Journal of MathematicsTopological 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 +4 more
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Extremal Values on the General Degree–Eccentricity Index of Unicyclic Graphs of Fixed Diameter
Journal of MathematicsFor 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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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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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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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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The inverse of the incidence matrix of a unicyclic graph [PDF]
Linear and Multilinear Algebra, 2022 The vertex-edge incidence matrix of a (connected) unicyclic graph G is a square matrix which is invertible if and only if the cycle of G is an odd cycle. A combinatorial formula of the inverse of the incidence matrix of an odd unicyclic graph was known.
Hessert, Ryan, Mallik, Sudipta
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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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ALGORITHMIC ASPECTS OF ROMAN GRAPHS [PDF]
Journal of Algebraic Systems, 2021 Let $G=(V, E)$ be a graph. A set $S \subseteq V$ is called a dominating set of $G$ if for every $v\in V-S$ there is at least one vertex $u \in N(v)$ such that $u\in S$.
A. Poureidi
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