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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, G. Ghorai
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On α-adjacency energy of graphs and Zagreb index [PDF]
AKCE International Journal of Graphs and Combinatorics, 2021 Let $A(G)$ be the adjacency matrix and $D(G)$ be the diagonal matrix of the vertex degrees of a simple connected graph $G$. Nikiforov defined the matrix $A_α(G)$ of the convex combinations of $D(G)$ and $A(G)$ as $A_α(G)=αD(G)+(1-α)A(G)$, for $0\leq α\leq 1$.
Shariefuddin Pirzada +3 more
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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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Maximum first Zagreb index of orientations of unicyclic graphs with given matching number [PDF]
Applied Mathematics and Computation, 2021 Let $D=(V,A)$ be a digraphs without isolated vertices. The first Zagreb index of a digraph $D$ defined as a summation over all arcs, $M_1(D)=\frac{1}{2}\sum\limits_{uv\in A}(d^{+}_{u}+d^{-}_v)$, where $d^{+}_u$(resp.
Jiaxiang Yang, H. Deng
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On the Zagreb Index of Random Recursive Trees [PDF]
Journal of Applied Probability, 2011 We investigate the Zagreb index, one of the topological indices, of random recursive trees in this paper. Through a recurrence equation, the first two moments of Zn, the Zagreb index of a random recursive tree of size n, are obtained. We also show that the random process {Zn − E[Zn], n ≥ 1} is a martingale.
Feng, Qunqiang, Hu, Zhishui
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On the first Zagreb Index of Polygraphs
Electronic Notes in Discrete Mathematics, 2014 Abstract One of the most popular topological indices is the Zagreb index, introduced by Gutman and Trinajstic in 1972, which is the sum of squares of degree sequence of a (chemical) graph G. In this paper, we obtain an upper bound for the Zagreb index of polygraphs, rotagraphs and fasciagraphs.
Hossein Shabani, Reza Kahkeshani
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On multiplicative sum Zagreb index of trees with fixed domination number
Journal of Mathematical Inequalities, 2023 . The multiplicative sum Zagreb index of a graph G is the product of the sums of degrees of pairs of adjacent vertices. In this paper, the maximal and minimal multiplicative sum Zagreb indices of trees with fi xed domination number are presented ...
Xiaol ng Sun, Yu in Gao, Jian ei Du
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The k-apex trees with minimum augmented Zagreb index [PDF]
Discrete Mathematics, 2022 For a connected graph $G$ on at least three vertices, the augmented Zagreb index (AZI) of $G$ is defined as $$AZI(G)=\sum_{uv\in E(G)}\left(\frac{d(u)d(v)}{d(u)+d(v)-2}\right)^{3},$$ being a topological index well-correlated with the formation heat of ...
Muhuo Liu +3 more
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BOUNDS ON THE HYPER-ZAGREB INDEX
Journal of Applied Mathematics & Informatics, 2016 Mahdieh Azari
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