Some Adriatic Indices of Dutch Windmill Graph Using Graph Operator (original) (raw)
Related papers
2018
Recently, A. M. Naji [13], introduced leap Zagreb indices of a graph based on the second degrees of vertices (number of their second neighbours). The first leap Zagreb index LM1(G) is equal to the sum of squares of the second degrees of the vertices, the second leap Zagreb index LM2(G) is equal to the sum of the products of the second degrees of pairs of adjacent vertices of G and the third leap Zagreb index LM3(G) is equal to the sum of the products of the first degrees with the second degrees of the vertices. In this paper, we computing Leap Zagreb indices of windmill graphs such as French windmill graph Fm n , Dutch windmill graph D m n , Kulli cycle windmill graph C m n+1, and Kulli path windmill graph Pm n+1. MSC: 05C05, 05C07, 05C35.
Indonesian Journal of Combinatorics
Dutch windmill graph [1, 2] and denoted by Dnm. Order and size of Dutch windmill graph are (n−1)m+1 and mn respectively. In this paper, we computed certain topological indices and polynomials i.e. Zagreb polynomials, hyper Zagreb, Redefined Zagreb indices, modified first Zagreb, Reduced second Zagreb, Reduced Reciprocal Randi´c, 1st Gourava index, 2nd Gourava index, 1st hyper Gourava index, 2nd hyper Gourava index, Product connectivity Gourava index, Sum connectivity Gourava index, Forgotten index, Forgotten polynomials, M-polynomials and some topological indices in term of the M-polynomials i.e. 1st Zagreb index, 2nd Zagreb index, Modified 2nd Zagreb, Randi´c index, Reciprocal Randi´c index, Symmetric division, Harmonic index, Inverse Sum index, Augmented Zagreb index for the semitotal-point graph and line graph of semitotal-point graph for Dutch windmill graph.
Computation of Topological Indices of Dutch Windmill Graph
Open Journal of Discrete Mathematics, 2016
In this paper, we compute Atom-bond connectivity index, Fourth atom-bond connectivity index, Sum connectivity index, Randic connectivity index, Geometric-arithmetic connectivity index and Fifth geometric-arithmetic connectivity index of Dutch windmill graph.
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International Journal of Analysis and Applications, 2022
One of the tools, to research and investigation the structural dependence of various properties and some activities of chemical structures and networks is the topological indices of graphs. In this research work, we introduce novel indices of graphs which they based on the uphill degree of the vertices termed as uphill Zagreb topological indices. Exact formulae of these new indices for some important and famous families of graphs are established.
Reformulated Zagreb Indices of Some Derived Graphs
Mathematics
A topological index is a numeric quantity that is closely related to the chemical constitution to establish the correlation of its chemical structure with chemical reactivity or physical properties. Miličević reformulated the original Zagreb indices in 2004, replacing vertex degrees by edge degrees. In this paper, we established the expressions for the reformulated Zagreb indices of some derived graphs such as a complement, line graph, subdivision graph, edge-semitotal graph, vertex-semitotal graph, total graph, and paraline graph of a graph.
Zagreb Indices of Some New Graphs
In this paper, we introduce Zagreb Indices of Some New Graphs. Exactly, first index, second index and forgotten index. New graphs are generated from the initial graphs by graph operations. We also created some possible applications on the Zagreb indices as special cases.
Some formulae for the Zagreb indices of graphs
2012
In this study, we first find formulae for the first and second Zagreb indices and coindices of certain classical graph types including path, cycle, star and complete graphs. Secondly we give similar formulae for the first and second Zagreb coindices.
Reformulated First Zagreb Index of Some Graph Operations
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 study the behavior of the reformulated first Zagreb index and apply our results to different chemically interesting molecular graphs and nano-structures.
Zagreb Indices of a New Sum of Graphs
Ural Mathematical Journal
The first and second Zagreb indices, since its inception have been subjected to an extensive research in the physio- chemical analysis of compounds. In [6] Hanyuan Deng et.al computed the first and second Zagreb indices of four new operations on a graph defined by M. Eliasi, B. Taeri in [4]. Motivated from this we define a new operation on graphs and compute the first and second Zagreb indices of the resultant graph. We illustrate the results with some examples.