Results 221 to 230 of about 19,763,523 (261)

First Zagreb index on a fuzzy graph and its application

Journal of Intelligent & Fuzzy Systems, 2021
The Zagreb index (ZI) is a very important graph parameter and it is extensively used in molecular chemistry, spectral graph theory, network theory and several fields of mathematics and chemistry. In this article, the first ZI is studied for several fuzzy graphs like path, cycle, star, fuzzy subgraph, etc. and presented an ample number of results. Also,
Sk Rabiul Islam, Madhumangal Pal
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CMMSE-on the first general Zagreb index

Journal of Mathematical Chemistry, 2017
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José M. Rodríguez, José L. Sánchez, José M. Sigarreta   +2 more
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A note on the first reformulated Zagreb index

Applied Mathematics and Computation, 2016
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Emina I. Milovanovic, Igor Z. Milovanovic, E. C. Dolicanin, Edin Glogic   +3 more
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On the second order first Zagreb index

2017
Summary: Inspired by the chemical applications of higher-order connectivity index (or Randić index), we consider here the higher-order first Zagreb index of a molecular graph. In this paper, we study the linear regression analysis of the second order first Zagreb index with the entropy and acentric factor of an octane isomers.
Basavanagoud, B, Patil, S., Deng, H. Y.
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Relation Between Wiener Index and First Zagreb Index with First Zagreb Coindex

International Journal of Mathematics and Computer Science
In this paper, we establish extremal results and bounds of Wiener index with respect to the sum of the first Zagreb index and the first Zagreb coindex of a graph given its minimum and maximum degrees together with its diameter. We have shown that nontrivial complete graphs correspond to extremal graphs.
Mohammad, Nurijam Hanna M., Patangan, Rachel M., Militante, Mae P., Abdulwahid, Faricia M., Fabillar, Edwin B.   +4 more
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On the first outdegree Zagreb index of a digraph

Discrete Mathematics
The 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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A note on the first Zagreb index and coindex of graphs

2021
Summary: Let \(G=(V,E)\), \(V=\{v_1,v_2,\dots,v_n\}\), be a simple graph with \(n\) vertices, \(m\) edges and a sequence of vertex degrees \(\Delta=d_1\geq d_2\geq\cdots\geq d_n=\delta\), \(d_i=d(v_i)\). If vertices \(v_i\) and \(v_j\) are adjacent in \(G\), it is denoted as \(i\sim j\), otherwise, we write \(i\nsim j\).
Milovanovic, Igor, Matejic, Marjan, Milovanovic, Emina, Khoeilar, Rana   +3 more
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On the first variable Zagreb index

2017
Summary: The first variable Zagreb index of graph \(G\) is defined as \(M_1^\lambda(G)=\sum_{x\in V(G)}d(v)^{2\lambda}\), where \(\lambda\) is a real number and \(d(v)\) is the degree of vertex \(v\). In this paper, some upper and lower bounds for the distribution function and expected value of this index in random increasing trees (recursive trees ...
Moradian, K., Kazemi, R., Behzadi, M.
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Bounds on first reformulated Zagreb index of graph

2017
Summary: The first reformulated Zagreb index \(EM_1(G)\) of a simple graph \(G\) is defined as the sum of the terms \((d_u+d_v-2)^2\) over all edges \(uv\) of \(G\). In this paper, the various upper and lower bounds for the first reformulated Zagreb index of a connected graph interms of other topological indices are obtained.
Pattabiraman, K, Santhakumar, A
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A Novel Weighted First Zagreb Index of Graph

2020
The Zagreb indices are the oldest among all degree-based topological indices. For a connected graph G, the first Zagreb index M1(G) is the sum of the term dG(u)+dG(v) corresponding to each edge uv in G, that is, M1 , where dG(u) is degree of the vertex u in G.
Jibonjyoti Buragohain, A. Bharali
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