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21 results on '"Togan, Muge"'

5. On the first Zagreb index and multiplicative Zagreb coindices of graphs

Author

Das Kinkar Ch., Akgunes Nihat, Togan Muge, Yurttas Aysun, Cangul I. Naci, and Cevik A. Sinan

Subjects
first zagreb index, first and second multiplicative zagreb coindex, narumi-katayama index, primary 05c07, secondary 05c12, Mathematics, QA1-939
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 dG(vi) is the degree of vertex vi in G. Recently Xu et al. introduced two graphical invariants and named as first multiplicative Zagreb coindex and second multiplicative Zagreb coindex, respectively. The Narumi-Katayama index of a graph G, denoted by NK(G), is equal to the product of the degrees of the vertices of G, that is, NK(G) = . The irregularity index t(G) of G is defined as the number of distinct terms in the degree sequence of G. In this paper, we give some lower and upper bounds on the first Zagreb index M1(G) of graphs and trees in terms of number of vertices, irregularity index, maxi- mum degree, and characterize the extremal graphs. Moreover, we obtain some lower and upper bounds on the (first and second) multiplicative Zagreb coindices of graphs and characterize the extremal graphs. Finally, we present some relations between first Zagreb index and Narumi-Katayama index, and (first and second) multiplicative Zagreb index and coindices of graphs.

Published
2016
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12. Harmonic Index and Zagreb Indices of Vertex-Semitotal Graphs.

Author

Gunes, Aysun Yurttas, Togan, Muge, Demirci, Musa, and Cangul, Ismail Naci

Subjects
*TOPOLOGICAL graph theory, *MOLECULAR structure, *MOLECULAR graphs, *SPECTRAL theory, *MOLECULAR models, *GRAPH theory
Abstract

Graph theory is one of the rising areas in mathematics due to its applications in many areas of science. Amongst several study areas in graph theory, spectral graph theory and topological descriptors are in front rows. These descriptors are widely used in QSPR/QSAR studies in mathematical chemistry. Vertex-semitotal graphs are one of the derived graph classes which are useful in calculating several physico-chemical properties of molecular structures by means of molecular graphs modelling the molecules. In this paper, several topological descriptors of vertex- semitotal graphs are calculated. Some new relations on these values are obtained by means of a recently defined graph invariant called omega invariant. [ABSTRACT FROM AUTHOR]

Published
2020
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16. New Formulae for Zagreb Indices.

Author

Cangul, Ismail Naci, Yurttas, Aysun, Togan, Muge, and Cevik, Ahmet Sinan

Subjects
CHEMICAL structure, CHEMICAL bonds, GRAPHIC methods, MOLECULAR structure, TOPOLOGY
Abstract

In this paper, we study with some graph descriptors also called topological indices. These descriptors are useful in determination of some properties of chemical structures and preferred to some earlier descriptors as they are more practical. Especially the first and second Zagreb indices together with the first and second multiplicative Zagreb indices are considered and they are calculated in terms of the smallest and largest vertex degrees and vertex number for some well-known classes of graphs. [ABSTRACT FROM AUTHOR]

Published
2017
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17. Zagreb and multiplicative Zagreb indices of r-subdivision graphs of double graphs.

Author

Togan, Muge, Yurttas, Aysun, and Cangul, Ismail Naci

Subjects
*TOPOLOGICAL spaces, *SUBGRAPHS, *TOPOLOGICAL graph theory, *INVARIANTS (Mathematics), *LAPLACIAN matrices
Abstract

Let G be a null, path, cycle, star, complete or a tadpole graph. In this paper, the first and second Zagreb and multiplicative Zagreb indices of subgraphs of the double graphs of G are obtained. [ABSTRACT FROM AUTHOR]

Published
2017

19. Properties of n-th Degree Bernstein Polynomials

Author

Cetin, Elif, primary, Ozbay, Hatice, additional, Togan, Muge, additional, Cangul, I. Naci, additional, Simos, Theodore E., additional, Psihoyios, George, additional, Tsitouras, Ch., additional, and Anastassi, Zacharias, additional

Published
2011
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21. Some Special Cases of the Minimal Polynomial of 2cos(π/q) over Q.

Author

Togan, Muge, Ozgur, Birsen, and Cangul, I. Naci

Subjects
*POLYNOMIALS, *NUMBER theory, *HECKE algebras, *FUCHSIAN groups, *GROUP theory, *DISCRETE groups
Abstract

The number λq = 2cosπ/q, q ∊ N, q ≥ 3, appears in the study of Hecke groups which are Fuchsian groups of the first kind, and in the study of regular polyhedra. Here we obtained some results on the values of the minimal polynomial of this number in modulo prime p. This results help in the calculation of the congruence subgroups of the Hecke groups which is an important problem in discrete group theory. [ABSTRACT FROM AUTHOR]

Published
2011
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