[PDF] Top 20 The Generalized Wiener Polarity Index of some Graph Operations

... Motivated by the definition of W G P ( ) , Ilić [3] recently defined ( d G k , ) to be the generalized Wiener polarity index W G k ( ) for its significance. As a matter of fact, Gutman [4] ... See full document

... of some complicated chemical ...known graph structure in Chemical graph ...of Generalized Thorn graphs as a generalization of thorn ...Zagreb index of some graph ... See full document

... the Wiener index and the Wiener polarity index of G4 H and G 5 H ...The Wiener index [11] defined as the sum of distances between all vertex pairs in a connected ...the ... See full document

... computed some exact formulae for the hyper-Wiener index of the join, Cartesian product, composition, disjunction and symmetric difference of ...graphs. Some more properties and applications of ... See full document

... Mathematical chemistry is a branch of theoretical chemistry for discus- sion and prediction of the molecular structure using mathematical methods without necessarily referring to quantum mechanics. In theoretical chem- ... See full document

... Schultz index), and the modified generalized degree distance is equal to the product-degree ...topological index is important and we try to obtain some new results related to this topological ... See full document

... connected graph with vertex and edge sets V(G) and E(G), ...a graph G, the degree of a vertex v is the number of edges incident to v , denoted by deg G v ...topological index Top(G) of a graph ... See full document

... A graph G on n vertices is said to be hyperenergeticif E >2n − ...A graph G on n vertices is said to be hypoenergetic if E(G) < ...on graph energy assume special significance ... See full document

... the Wiener polarity in- dex and the Wiener index of generalized Petersen graph GP (n, k) are obtained; for k ∈ [2], the Szeged index, the edge-Szeged index, and the ... See full document

... The Wiener index is a graph invariant that has found extensive application in ...the Wiener polynomial, who’s derivate is a q-analog of the Wiener index was ...[The Wiener ... See full document

... A graph is a collection of points and lines connecting ...a graph are also called vertices and edges ...connected graph is a graph such that there is a path between all pairs of ...simple ... See full document

... A vertex ∈ ( ), is said to be equidistant from the edge e = uv of if ( , ) = ( , ). The number of equidistant vertices of e is denoted by ( ). Let uv be an edge of . Define the sets ( , ) = { ∈ ( )| ( , ) < ( , )} and ... See full document

... A graph G = ( V G ( ) ( ) , E G ) is said to be a product cordial graph if there exists a function f V G : ( ) { } → 0 ,1 with each edge uv assign the label f u f v ( ) ( ) , such that the number of ... See full document

... Proof: Let T be any Kragujevac tree T of degree d ≥ 2. Then by Lemma 1, there exist four minimal dominating sets namely D 1 , D 2 , D 3 and D 4 . Hence by the definition of MD (G ) , the vertex set of the minimal ... See full document

... molecular graph. A molecular graph is a collection of points representing the atoms in the molecule and set of lines representing the covalent ...in graph theory ...is Wiener index. It ... See full document

... fan graph, star graph, bistar graph, helm graph, and friendship graph are investigated and their chromatic indices are ...chromatic index determines the minimum number of color ... See full document

... a graph is represented as 𝐺𝐺 = (𝑉𝑉, 𝐸𝐸) where 𝑉𝑉 is the set of vertices and 𝐸𝐸 is the set of ...connected graph without loops or multiple edges with 𝑛𝑛 vertices, denoted by 1,2, … , 𝑛𝑛 ... See full document

... If is acyclic and connected graph, then is a tree. Any tree with at least two vertices has at least two pendent vertices. The set of all −vertex trees is denoted by ( ). In chemical graph theory, a ... See full document

... regular graph that is not ...distance-balanced graph by two graphs which are not ...regular graph then by the above proposition, G'  G is distance-balanced (note that G can be not ... See full document

... the graph. A connected graph without a cutvertex is called a non-separable ...a graph is a maximal non-separable subgraph. A cycle is a connected graph (or subgraph) in which every vertex is ... See full document