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UPHILL ZAGREB INDICES OF SOME GRAPH OPERATIONS FOR CERTAIN GRAPHS
SALEH, ANWAR,BAZHEAR, SARA,MUTHANA, NAJAT The Korean Society for Computational and Applied M 2022 Journal of applied mathematics & informatics Vol.40 No.5-6
The topological indices are numerical parameters which determined the biological, physical and chemical properties based on the structure of the chemical compounds. One of the recently topological indices is the uphill Zagreb indices. In this paper, the formulae of some uphill Zagreb indices for a few graph operations of some graphs have been derived. Furthermore, the precise formulae of those indices for the honeycomb network have been found along with their graphical profiles.
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.
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>
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.
Some new topological indices of Aspirin
S.A. Wazzan 장전수학회 2020 Proceedings of the Jangjeon mathematical society Vol.23 No.1
Acetylsalicylic acid (ASA), commonly known as Aspirin, is a medicinal drug prescribed to treat pain, fever, or in ammation. Topo- logical indices are graph invariants computed by the distance or degree of vertices of the molecular graph. In chemical graph theory, topolog- ical indices have been successfully used to describe the structures and predict certain physicochemical properties of chemical compounds. In this paper, we compute new topological indices, including the first and second entire Zagreb indices, the first and second Zagreb eccentricity indices, the Zagreb degree eccentricity indices, first and second locat- ing indices, and Sanskruti index of Aspirin. In addition, some other topological indices are calculated.
Complete characterization of graphs for direct comparing Zagreb indices
Horoldagva, B.,Das, K.Ch.,Selenge, T.A. North Holland ; Elsevier Science Ltd 2016 Discrete Applied Mathematics Vol.215 No.-
<P>The classical first and second Zagreb indices of a graph G are defined as M-1(G) = Sigma(v is an element of V) d(G)(v)(2) and M-2(G) = Sigma(uv is an element of E(G)) d(G)(u) d(G)(V), where d(G)(v) is the degree of the vertex v of graph G. Recently, Furtula et al. (2014) studied the difference between the Zagreb indices and mentioned a problem to characterize the graphs for which M-1(G) > M-2 (G) or M-1(G) < M-2 (G) or M-1(G) = M-2 (G). In this paper we completely solve this problem. (C) 2016 Elsevier B.V. All rights reserved.</P>
MAXIMUM ZAGREB INDICES IN THE CLASS OF k-APEX TREES
SELENGE, TSEND-AYUSH,HOROLDAGVA, BATMEND The Kangwon-Kyungki Mathematical Society 2015 한국수학논문집 Vol.23 No.3
The first and second Zagreb indices of a graph G are defined as $M_1(G)={\sum}_{{\nu}{\in}V}d_G({\nu})^2$ and $M_2(G)={\sum}_{u{\nu}{\in}E(G)}d_G(u)d_G({\nu})$. where $d_G({\nu})$ is the degree of the vertex ${\nu}$. G is called a k-apex tree if k is the smallest integer for which there exists a subset X of V (G) such that ${\mid}X{\mid}$ = k and G-X is a tree. In this paper, we determine the maximum Zagreb indices in the class of all k-apex trees of order n and characterize the corresponding extremal graphs.
Relation between signless Laplacian energy, energy of graph and its line graph
Das, K.Ch.,Mojallal, S.A. North Holland [etc.] 2016 Linear Algebra and its Applications Vol.493 No.-
<P>The energy of a simple graph G, epsilon(G), is the sum of the absolute values of the eigenvalues of its adjacency matrix. The energy of line graph and the signless Laplacian energy of graph G are denoted by epsilon(L-G) (L-G is the line graph of G) and LE+ (G), respectively. In this paper we obtain a relation between epsilon(LG) and LE+(G) of graph G. From this relation we characterize all the graphs satisfying epsilon(L-G) = LE+ (G) + 4m/n - 4. We also present a relation between epsilon(G) and epsilon(L-G). Moreover, we give an upper bound on epsilon(L-G) of graph G and characterize the extremal graphs. (C) 2015 Elsevier Inc. All rights reserved.</P>