[PDF] Top 20 EDGE-ZAGREB INDICES OF GRAPHS

... graph indices have been defined and studied by many mathematicians and chemists as most graphs are generated from molecules by replacing atoms with vertices and bonds with ...of graphs modelling real ... See full document

... of Zagreb indices and Zagreb polynomials are analysed for nanostar dendrimers us- ing edge partition based on degree of vertices of the edges of the corresponding chemical ...First ... See full document

... first Zagreb index of a graph G is the sum of squares of the vertex degrees in a graph and the second Zagreb index of G is the sum of products of degrees of adjacent vertices in ...an edge in G is ... See full document

... second Zagreb indices of a graph denoted by M G 1 ( ) and M G 2 ( ) , respectively, are degree based topological indices introduced by Gutman and Trinajstić ...two indices are defined as ... See full document

... E G e e e , thus possessing n vertices and m edges. The degree d v ( ) of the vertex v V G  ( ) is the number of first neighbors of v. The edge of the graph G, connecting the vertices u and v, will be denoted by ... See full document

... INTRODUCTION: In this paper, we only consider an undirected graph without loops and multiple edges. Let G be a graph, we denote V (G) and E(G) the vertex set and edge set of G, respectively. An edge uv is ... See full document

... Definition 2.1. [1] Let G be a simple graph of order n. Then R G ( ) be the graph obtained from G by adding a new vertex corresponding to each edge of G and by joining each new vertex to the end points, of the ... See full document

... of Zagreb index. In this paper, we introduce a new invariant the K-edge index which is defined as the sum of the cubes of the edge degrees of a ...Keywords: Zagreb indices, reformulated ... See full document

... molecular graphs known as kenographs, see [13] for more in- ...topological indices such as Wiener-type indices [2], Szeged, vertex PI, first and second Zagreb in- dices [18], weighted PI index ... See full document

... topological indices like the Forgotten index, Zagreb and Banhatti indices of some derived graphs such as line graph, subdivision graph, vertex-semitotal graph, edge-semitotal graph and ... See full document

... Suppose G and H are two graphs. The union G ∪ H is a graph with the vertex set V (G) ∪ V (H) and edge set E(G) ∪ E(H). The join of G and H is a graph with the same vertex set as G ∪ H and E(G + H) = E(G) ∪ ... See full document

... Throughout the paper we consider only simple finite graphs. V (G) and E (G) are respectively the set of vertices and set of edges of a graph G. The degree of a vertex u ∈ V (G) is denoted by d G (u), if their is ... See full document

... Proof. The proof of all maximal cases is similar to the proof of the last theorem. For the seventh minimal, it should be noted that by adding a new edge, the resulted graph is not overfull. Let the seventh, ... See full document

... each edge of G. Subdivision graphs are used to obtain several mathematical and chemical properties of more complex graphs from more basic graphs and there are many results on these ...each ... See full document

... e graphs considered in this paper are simple connected graph with vertex set V and edge set ...second Zagreb indices. Za- greb indices are defined as ... See full document

... simple graphs, that is finite and undirected graphs without loops and multiple ...and edge set, respectively. An edge of G, connecting the vertices u and v will be denoted by ... See full document

... Topological indices have some major classes but among these classes degree based topological indices have prominent role in chemical graph ...the edge version of some important degree based ... See full document

... Ashrafi, Vertex and edge PI indices of Cartesian product graphs, Discrete Appl.. Ashrafi, A matrix method for computing Szeged and vertex PI indices of join and composition of graphs,[r] ... See full document

... A molecular graph is a graph such that its vertices correspond to the atoms and the edges to the bonds. A topological index is a numerical parameter mathematically derived from the graph structure. In chemical science, ... See full document

... topological indices of molecular graphs are widely used for establishing correlations between the structure of a molecular compound and its physico- chemical properties or biological activity ...These ... See full document