Results 21 to 30 of about 572,605 (265)
The First Zagreb Index of the Zero Divisor Graph for the Ring of Integers Modulo Power of Primes
Malaysian Journal of Fundamental and Applied Sciences, 2023 Let be a simple graph with the set of vertices and edges. The first Zagreb index of a graph is defined as the sum of the degree of each vertex to the power of two. Meanwhile, the zero divisor graph of a ring , denoted by , is defined as a graph with its
G. Semil Ismail +3 more
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Extremal Graphs with Respect to the Modified First Zagreb Connection Index [PDF]
2018 20th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC), 2018 Topological indices (TIs) have an important role in studying properties of molecules. A main problem in mathematical chemistry is finding extreme graphs with respect to a given TI. In this paper extremal graphs with respect to the modified first Zagreb connection index for trees in general and for trees with given number of pendants, for unicyclic ...
Ducoffe, Guillaume +4 more
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First Entire Zagreb Index of Fuzzy Graph and Its Application
Axioms, 2023 The first entire Zagreb index (FEZI) is a graph parameter that has proven to be essential in various real-life scenarios, such as networking businesses and traffic management on roads.
Umapada Jana, Ganesh Ghorai
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On the Reformulated Multiplicative First Zagreb Index of Trees and Unicyclic Graphs
Discrete Dynamics in Nature and Society, 2021 The multiplicative first Zagreb index of a graph H is defined as the product of the squares of the degrees of vertices of H. The line graph of a graph H is denoted by LH and is defined as the graph whose vertex set is the edge set of H where two vertices
Akbar Ali +4 more
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Computing Reformulated First Zagreb Index of Some Chemical Graphs as an Application of Generalized Hierarchical Product of Graphs [PDF]
Open Journal of Mathematical Sciences, 2017 The generalized hierarchical product of graphs was introduced by L. Barri\'ere et al in 2009. In this paper, reformulated first Zagreb index of generalized hierarchical product of two connected graphs and hence as a special case cluster product of graphs
Nilanjan De
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The Bounds for the First General Zagreb Index of a Graph
Universal Journal of Mathematics and Applications, 2021 The first general Zagreb index of a graph $G$ is defined as the sum of the $\alpha$th powers of the vertex degrees of $G$, where $\alpha$ is a real number such that $\alpha \neq 0$ and $\alpha \neq 1$.
Rao Li
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Extremal Chemical Trees of the First Reverse Zagreb Alpha Index [PDF]
Mathematics Letters, 2017 Topological indices have important effect to develop chemical sciences by using graph invariants. The Zagreb indices are the most used topological indices in mathematical chemistry literature. Novel forms of Zagreb indices have been extensively defined in recent times.
Süleyman Ediz
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On First Zagreb index, \({\tau}\)-path-coverable and \({\tau}\)-edge-Hamiltonian graphs [PDF]
Ars Comb.Given a connected graph \(H\), its first Zagreb index \(M_{1}(H)\) is equal to the sum of squares of the degrees of all vertices in \(H\). In this paper, we give a best possible lower bound on \(M_{1}(H)\) that guarantees \(H\) is \(\tau\)-path-coverable
Mingqiang An, Runli Tian, Huiya Yan
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The first Zagreb index, the algebraic connectivity and some Hamiltonian properties of graphs [PDF]
Journal of Combinatorial Mathematics and Combinatorial ComputingThe first Zagreb index of a graph \(G\) is defined as \(\sum\limits_{u \in V} d_G^2(u)\), where \(d_G(u)\) is the degree of vertex \(u\) in \(G\). The algebraic connectivity of a graph \(G\) is defined as the second smallest eigenvalue of the Laplacian ...
Rao Li
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Extremal chemical trees of the first reverse Zagreb beta index [PDF]
Notes on Number Theory and Discrete Mathematics, 2018 The reverse vertex degree of a vertex v of a simple connected graph G defined as c(v) = Delta - d(v) + 1, where Delta denotes the largest of all degrees of vertices of G and d(v) denotes the number of edges incident to v. The first reverse Zagreb beta index of a simple connected graph G defined as CM1 beta(G) = Sigma(uv is an element of E(G))(c(u) + c ...
Semiz, Mesut, Ediz, Süleyman
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