[PDF] Top 20 An Upper Bound on the First Zagreb Index in Trees

... In this paper, G is a simple connected graph with vertex set V = V(G) and edge set E = E(G). The order |V| of G is denoted by n = n(G). For every vertex v  V , the open neighborhood N ( v ) is the set { u  V ( G ) | uv ... See full document

... the first general Zagreb index of G as follows ( ) = ∑ ∈ ( ) ( ) ...all trees with the first three smallest and largest values of the first general Zagreb index, ... See full document

... derives upper bound scores for non- leaf entries in the object tree, and prunes those that cannot lead to better ...(and upper bound scores of non-leaf ...feature trees to obtain ... See full document

... Kirchhoff index is not always possible, it is useful to know approximating expressions, ...i.e. upper and lower bounds and corresponding extremal ...and upper bounds for K f (G) of a connected ... See full document

... lower bound in Theorem 2.1 and an upper bound in Theorem ...and upper bounds for the moment generating function and moments are very ... See full document

... some upper bounds on irregularity for trees, bipartite, and triangle-free ...the first Zagreb index M and the second Zagreb index M of are defined as M (G) = ∑ ∈ ( ) d (u) ... See full document

... the bound on the distance k-domination number of a connected graph is an attractive ...an upper bound for the distance k-domination num- ber of a tree is ... See full document

... Reformulated Zagreb index, particularly its upper and lower bounds has attracted recently threat tension of many mathematicians and computer scientists, in [2, 10, 12, 13, 14, 19, ...various ... See full document

... the first reformulated Zagreb index of graphs with connectivity at most k and characterized the corresponding extremal ...on Zagreb and reformulated Zagreb indices of simple ... See full document

... The first variable Zagreb index of graph G is defined as ( ) = ∑ ∈ ( ) ( ) , where  is a real number and d(v) is the degree of vertex ...and upper bounds for the expected value and ... See full document

... modified first and second Zagreb indices, harmonic index and augmented Zagreb index for certain networks like silicate networks and honeycomb ... See full document

... Proof. Let n = 2r + 1. There are four kind of edges in L. The vertices of the first kind of edges have degree n 2 + 1 = r + 1 and and the reverse degree of these vertices are r + 1. The vertices of the second kind ... See full document

... In this section, we focus on the structure of hydrocarbon structures and counting the First Multiple Zagreb index and Second Multiple Zagreb index of Polycyclic Aromatic Hydrocarbons ... See full document

... topological index is a numerical quantity based on the characteristics of various invariants or molecular ...computes Zagreb polynomials and redefined first, second and third Zagrebindices of Bismuth ... See full document

... finite index. If one can calculate an upper bound for this index, then by using the method of the next lemma one can obtain an upper bound for the commutator length of a finitely ... See full document

... Katayama index (NK) are defined as product of squares of vertex degrees and usual product of all vertex degrees of graph G ...determine upper bound of NK index of G with maximum edge ... See full document

... topological index of a graph is a number related to a graph which is invariant under graph automorphisms and is a numeric quantity from the structural graph of a ...the Zagreb topological index ... See full document

... general Zagreb index or (a, b)-Zagreb ...this index. Based on multiplicative version second Zagreb index and multiplicative version sum Zagreb index in this paper, ... See full document

... multiplicative Zagreb indices of graph operations, Journal of Inequalities and Applications, 90 (2013) ...multiplicative Zagreb coindex with some graph invariants, ... See full document

... Let G be simple graph. The first Zagreb index is the sum of squares of degree of vertices and second Zagreb index is the sum of the products of the degrees of pairs of[r] ... See full document