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RISS 인기검색어
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- 저자 : A. Sinan Cevik (검색결과 4 건)
- 무료
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On the first Zagreb index and multiplicative Zagreb coindices of graphs
Das, Kinkar Ch.,Akgunes, Nihat,Togan, Muge,Yurttas, Aysun,Cangul, I. Naci,Cevik, A. Sinan De Gruyter Open 2016 Analele Stiintifice ale Universitatii Ovidius Cons Vol.24 No.1
<P>For a (molecular) graph G with vertex set V (G) and edge set E(G), the first Zagreb index of G is defined as M-1(G) = Sigma v(i is an element of V(G))d(C)(v(i))(2), where d(G) (v(i)) is the degree of vertex v(i), in G. Recently Xu et al. introduced two graphical invariants (Pi) over bar (1) (G) = Pi v(i)v(j is an element of E(G)) (dG (v(i))+dG (v(j))) and (Pi) over bar (2)(G) = Pi(vivj is an element of E(G)) (dG (v(i))+dG (v(j))) 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) = Pi(n)(i=1) d(G) (v(i)). The irregularity index t(G) of G is defined as the num=1 ber of distinct terms in the degree sequence of G. In this paper, we give some lower and upper bounds on the first Zagreb index M-1(G) of graphs and trees in terms of number of vertices, irregularity index, maximum 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 NarumiKatayama index, and (first and second) multiplicative Zagreb index and coindices of graphs.</P>
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VL Status Index and Co-index of Connected Graphs
V. Lokesha,S. Suvarna,A. Sinan Cevik 장전수학회 2021 Proceedings of the Jangjeon mathematical society Vol.24 No.3
The status σG(u) of a vertex u in a connected graph G is defined as the sum of the distances between u and all other vertices of G. In this paper some relations over VL status index and VL status co-index of connected graphs are established. Furthermore distinguished examples for k-transmission regular graphs and nanostructures of VL status indices are computed.
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Operations on Dutch windmill graph of topological indices
V.Lokesha,Sushmitha Jain,T. Deepika,A. Sinan Cevik 장전수학회 2018 Proceedings of the Jangjeon mathematical society Vol.21 No.3
Topological indices are well studied in recent years. These are useful tools in studying Quantitative Structure Activity Relationship (QSAR) and Quantitative Structure Property Relationship (QSPR). The main goal of this paper is to concentrate the investigation on generalized version of Dutch windmill graph of certain graph operators in terms of topological indices, for instance, symmetric division deg index, rst and second Zagreb indices.
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Some properties on the tensor product of graphs obtained by monogenic semigroups
Akgunes, N.,Das, K.Ch.,Sinan Cevik, A. Elsevier [etc.] 2014 Applied mathematics and computation Vol.235 No.-
In Das et al. (2013) [8], a new graph Γ(S<SUB>M</SUB>) on monogenic semigroups S<SUB>M</SUB> (with zero) having elements {0,x,x<SUP>2</SUP>,x<SUP>3</SUP>,...,x<SUP>n</SUP>} has been recently defined. The vertices are the non-zero elements x,x<SUP>2</SUP>,x<SUP>3</SUP>,...,x<SUP>n</SUP> and, for 1≤i,j≤n, any two distinct vertices x<SUP>i</SUP> and x<SUP>j</SUP> are adjacent if x<SUP>i</SUP>x<SUP>j</SUP>=0 in S<SUB>M</SUB>. As a continuing study, in Akgunes et al. (2014) [3], it has been investigated some well known indices (first Zagreb index, second Zagreb index, Randic index, geometric-arithmetic index, atom-bond connectivity index, Wiener index, Harary index, first and second Zagreb eccentricity indices, eccentric connectivity index, the degree distance) over Γ(S<SUB>M</SUB>). In the light of above references, our main aim in this paper is to extend these studies over Γ(S<SUB>M</SUB>) to the tensor product. In detail, we will investigate the diameter, radius, girth, maximum and minimum degree, chromatic number, clique number and domination number for the tensor product of any two (not necessarily different) graphs Γ(S<SUB>M</SUB><SUP>1</SUP>) and Γ(S<SUB>M</SUB><SUP>2</SUP>).
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