Results 1 to 10 of about 572,605 (265)

Some new bounds on the first Zagreb index [PDF]

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, Marjan M. Matejic, Igor Z. Milovanovic, Emina I. Milovanovic, Serife Burcu Bozkurt Altındag   +4 more
doaj   +4 more sources

Reformulated First Zagreb Index of Some Graph Operations [PDF]

Mathematics, 2015
The reformulated Zagreb indices of a graph are obtained from the classical Zagreb indices by replacing vertex degrees with edge degrees, where the degree of an edge is taken as the sum of degrees of the end vertices of the edge minus 2. In this paper, we
Nilanjan De, Sk. Md. Abu Nayeem, Anita Pal   +2 more
doaj   +8 more sources

On the first Zagreb index and multiplicative Zagreb coindices of graphs [PDF]

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2016
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 dG(vi) is the degree of vertex vi in G. Recently Xu et al. introduced two graphical invariants and named as first multiplicative Zagreb
Das Kinkar Ch., Akgunes Nihat, Togan Muge, Yurttas Aysun, Cangul I. Naci, Cevik A. Sinan   +5 more
doaj   +9 more sources

The first Zagreb index conditions for Hamiltonian and traceable graphs [PDF]

Open Journal of Discrete Applied Mathematics
The first Zagreb index of a graph is one of the most important topological indices in chemical graph theory. It is also an important invariant of general graphs. The first Zagreb index of a graph is defined as the sum of the squares of the degrees of the vertices in the graph.
Rao Li
semanticscholar   +3 more sources

Maximal first Zagreb index of trees with given Roman domination number

AIMS Mathematics, 2022
<abstract><p>The first Zagreb index of graphs is defined to be the sum of squares of degrees of all the vertices of graphs. It drew a great deal of attention in the past half-century. In this paper, we study the relationship between the first Zagreb index and Roman domination number of graphs.
Zhibin Du, Ayu Ameliatul Shahilah Ahmad Jamri, Roslan Hasni, Doost Ali Mojdeh   +3 more
semanticscholar   +4 more sources

SHARP BOUNDS FOR THE FIRST ZAGREB INDEX AND FIRST ZAGREB COINDEX [PDF]

Miskolc Mathematical Notes, 2015
Milovanovic, Emina, Milovanovic, Igor
core   +5 more sources

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
semanticscholar   +4 more sources

Some Upper Bounds on the First General Zagreb Index [PDF]

Journal of Mathematics, 2022
The first general Zagreb index MγG or zeroth-order general Randić index of a graph G is defined as MγG=∑v∈Vdvγ where γ is any nonzero real number, dv is the degree of the vertex v and γ=2 gives the classical first Zagreb index.
Muhammad Kamran Jamil, Aisha Javed, Ebenezer Bonyah, Iqra Zaman   +3 more
doaj   +3 more sources

First Zagreb Index and its Characteristics on Neutrosophic Graph

International Journal on Robotics, Automation and Sciences
Topological indices mark an irreplaceable place for applications in crisp and fuzzy graphs. These indices are extended to the neutrosophic graphical idea to rectify the imprecise values or information acquired before, since the uncertain cases are organized and allocated as a separate membership called "indeterminacy".
Vetrivel Govindan, Mullai Murugappan, Greinggrai Rajchakit, Sangavi Meyyappan, Surya R.   +4 more
semanticscholar   +4 more sources

New Sharp lower bounds for the first Zagreb index [PDF]

Scientific Publications of the State University of Novi Pazar Series A: Applied Mathematics, Informatics and mechanics, 2016
The first Zagreb index M1(G) defined as the sum of squares of the degrees of the vertices. In this paper we compare and analyze numerous lower bounds for the first Zagreb index involving the number of vertices, the number of edges and the maximum and minimum vertex degree.
T. Mansour, M.A. Rostami, E. Suresh, G.B.A. Xavier   +3 more
semanticscholar   +3 more sources