Results 11 to 20 of about 4,394,235 (151)
On neighborhood Zagreb index of product graphs. [PDF]
J Mol Struct, 2021 There is powerful relation between the chemical behaviour of chemical compounds and their molecular structures. Topological indices defined on these chemical molecular structures are capable to predict physical properties, chemical reactivity and biological activity.
Mondal S, De N, Pal A.
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Hyper-Zagreb index in fuzzy environment and its application. [PDF]
HeliyonThe Zagreb indices (ZIs) are important graph invariants that are used extensively in many different fields in mathematics and chemistry, such as network theory, spectral graph theory, fuzzy graph theory (FGT) and molecular chemistry, etc. The hyper-ZI is
Islam SR, Mohsin BB, Pal M.
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Mathematics, 2023 Degree sequence measurements on graphs have attracted a lot of research interest in recent decades. Multiplying the degrees of adjacent vertices in graph Ω provides the multiplicative first Zagreb index of a graph.
Sakander Hayat, Hayat Sakander
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Bounds for the augmented Zagreb index
Theory and Applications of Graphs, 2023 Summary: The augmented Zagreb index (AZI for short) of a graph \(G\), introduced by \textit{B. Furtula} et al. [J. Math. Chem. 48, No. 2, 370--380 (2010; Zbl 1196.92050)] is defined as AZI\((G)=\sum_{v_iv_j\in E(G)}\left(\frac{d(v_i)d(v_j)}{d(v_i)+d(v_j)-2}\right)^3\), where \(E(G)\) is the edge set of \(G\), and \(d(v_i)\) denotes the degree of the ...
qingcuo, Ren +3 more
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On the first Zagreb index of graphs with Self-Loops
AKCE International Journal of Graphs and Combinatorics, 2023 AbstractSome of the most comprehensively studied degree-based topological indices are the Zagreb indices. The first Zagreb index [Formula: see text] of a graph G is defined as the sum of squares of the degrees of the vertices. Let [Formula: see text] and let [Formula: see text] be the graph obtained from the simple graph G, by attaching a self-loop to ...
Shashwath S. Shetty, Arathi Bhat K.
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On the first outdegree Zagreb index of a digraph
Discrete MathematicsThe paper provides a thorough exploration of the first outdegree Zagreb index $(Zg^+(D))$ for a directed graph $(D)$. The authors successfully establish various upper and lower bounds for $(Zg^+(D))$ in terms of the number of vertices $(n)$ and arcs $(a)$, offering a comprehensive understanding of the index's behavior.
Hilal A. Ganie, Shariefuddin Pirzada
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Some New Bounds on the First Zagreb Index
Electronic Journal of Mathematics, 2021 In this paper, new inequalities involving the first Zagreb index, inverse degree index and modified first Zagreb index are established. Some new and old bounds on the first Zagreb index are given as corollaries of the obtained inequalities.
Stefan D. Stankov +4 more
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A Novel/Old Modification of the First Zagreb Index [PDF]
Molecular Informatics, 2018 AbstractIn the seminal paper [I. Gutman, N. Trinajstić, Chem. Phys. Lett. 1972, 17, 535–538], it was shown that total electron energy ( ) of any alternant hydrocarbon depends on the sum of the squares of the degrees of the corresponding molecular graph. Nowadays, this sum is known as the first Zagreb index.
Akbar Ali, Nenad Trinajstić
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The First Zagreb Index, The Wiener Index, and The Gutman Index of The Power of Dihedral Group
CAUCHY, 2023 Research on graphs combined with groups is an interesting topic in the field of combinatoric algebra where graphs are used to represent a group. One type of graph representation of a group is a power graph.
Evi Yunartika Asmarani +5 more
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On the first Zagreb index and multiplicative Zagreb coindices of graphs [PDF]
Analele Universitatii "Ovidius" Constanta - Seria Matematica, 2016 Abstract For a (molecular) graph G with vertex set V (G) and edge set E(G), the first Zagreb index of G is defined as , where d G (v i ) is the degree of vertex vi in G.
Das, Kinkar Ch +5 more
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