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All versions of Zagreb indices and coindices of subdivision graphs of certain graph types
Muge TOGAN,Aysun YURTTAS,Ismail Naci CANGUL 장전수학회 2016 Advanced Studies in Contemporary Mathematics Vol.26 No.1
In this paper, we nd formulae for ten mostly used types of Zagreb indices for the subdivision graphs of some well-known classes of graphs.
Inverse problem for the first entire Zagreb index
Muge TOGAN,Aysun YURTTAS,Ismail Naci CANGUL 장전수학회 2019 Advanced Studies in Contemporary Mathematics Vol.29 No.2
The inverse problem for topological graph indices is about the exis- tence of a graph having its index value equal to a given non-negative integer. In this paper, we study the problem for the rst entire Zagreb index. We will rst show that the rst entire Zagreb index must be even for any graph G, and can take all positive even integer values except 4; 6; 10; 12; 14; 18; 20; 22; 26; 28; 30; 36; 38 and 46.
RELATIONS BETWEEN THE FIRST AND SECOND ZAGREB INDICES OF SUBDIVISION GRAPHS
Aysun YURTTAS,Muge TOGAN,Ismail Naci CANGUL 장전수학회 2018 Advanced Studies in Contemporary Mathematics Vol.28 No.3
The first and second Zagreb indices of a graph are two of the topological invariants used in molecular calculations by Mathematicians and Chemists. First Zagreb index and multiplicative Zagreb indices, all versions of Zagreb indices of subdivision graphs, Zagreb indices of the line graphs of the subdivision graphs, Zagreb indices of subdivision graphs of double graphs, multiplicative Zagreb indices of graph operations were cal- culated and as a generalisation, the authors determined the multiplicative Zagreb indices of the r-subdivision of double graphs. In this paper, we ob- tain numerous new relations between the first and second Zagreb indices of the subdivision graphs of certain graph types.
Zagreb indices of graphs with added edges
Aysun YURTTAS,Muge TOGAN,Naci CANGUL 장전수학회 2018 Proceedings of the Jangjeon mathematical society Vol.21 No.3
Edge deletion and addition to a graph is an important combinatorial method in Graph Theory which enables one to calculate some properties of a graph by means of similar graphs. In this paper, as a sequel to a recent paper on edge deletion, we consider the change in the first and second Zagreb indices of a simple graph G when an arbitrary edge is added. This can be used to calculate the first and second Zagreb indices of larger graphs in terms of the Zagreb indices of smaller graphs. As some examples, some inequalities for the change of Zagreb indices for path, cycle, star, complete, complete bipartite and tadpole graphs are given.
Zagreb indices and multiplicative Zagreb indices of subdivision graphs of double graphs
Aysun YURTTAS,Muge TOGAN,Ismail Naci CANGUL 장전수학회 2016 Advanced Studies in Contemporary Mathematics Vol.26 No.3
Let G be a null, path, cycle, star, complete or a tadpole graph. In this paper, the rst and second Zagreb and multiplicative Zagreb indices of subgraphs of the double graphs of G are obtained.
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>