[PDF] Top 20 Modified Generalized Degree Distance of Some Graph Operations

... Proof. The parts 1) - 5) are consequence of definitions and some well-known results of the book of Imrich and Klavzar [18]. For the proof of 6) - 10) we refer to [21]. ■ For a given graph G i , we denote n ... See full document

... the generalized degree distance of ...introduce generalized and modified generalized degree distance Polynomials of graphs, such that their first derivatives at x = ... See full document

... and graph invariants based on the distances between the vertices of a graph are widely used in theoretical chemistry to establish relations between the struc- ture and the properties of ...connected ... See full document

... undirected graph of order n. We begin by recalling some standard definitions that we need throughout this ...The degree of v in G denoted by deg(v), is the size of its open ...The distance ... See full document

... connected graph with n vertices. The 2- degree of a vertex v in G is the number of vertices which are at distance two from v in ...of degree and 2-degree of all vertices in ...of ... See full document

... several graph polynomials like PI polynomial [3], Tutte polynomial [14], matching polynomial [15,20], Schultz polynomial [25], Zang-Zang polynomial [46], ...determining distance-based topological indices ... See full document

... the degree distance is a degree-weight version of the Wiener ...the degree distance DD(G) have been put forward in past decades and they mainly deal with extreme properties of ...unique ... See full document

... In this paper, we present explicit formulas for this new graph invariant of the Cartesian product, composition, join, disjunction and symmetric difference of graphs and introduce general[r] ... See full document

... connected graph. The generalized polarity Wiener index of G is defined as the number of unordered pairs of vertices of G whose distance is ...k. Some formulas are obtained for computing the ... See full document

... A graph with p points and q edges is denoted by ...connected graph G, the monophonic distance d m ( u , v ) from u to v is defined as the length of a longest u-v monophonic path in ...a graph ... See full document

... This paper is organized as follows. In Section 2, some auxiliary lemma are given. In Section 3, we obtain formulas for resistance distances of R-vertex corona and R-edge corona of two arbitrary graphs. In Section ... See full document

... The open neighborhood of an edge e ∈ E denoted by N (e ) is the set of all edges adjacent to e in G If . e = ( u , v ) is an edge in G , the degree of e denoted by deg e is ( ) given by deg ( e ) = deg ( u ) + ... See full document

... Abstract. Binary codes from graphs have been studied widely since 1960’s. Matrices associated with the graphs were considered as a good tool to construct codes from graphs. Incidence matrix, Adjacency matrix, cut set ... See full document

... in graph theory is [1]. A molecular graph is a simple finite graph such that its vertices correspond to the atoms and the edges to the ...a graph G is a number related to a graph which ... See full document

... a graph G is a graph that can be obtained from G by a sequence of edges ...a graph G for which G −−− is ...complete graph, the cycle, the path of order n are denoted K C P n , n , n , ... See full document

... give some examples and showed that fixed point theorems from ordinary metric spaces cannot be applied in the setting of cone metric spaces whenever the cone is ... See full document

... ≤ ... ≤ λ n d (x, f x) = λ n r (x) . Lemma 4.4. Let (X, d) be a complete metric space endowed with a graph G. Suppose that f : X → X is a Hardy-Rogers G-contraction with constant α, β, γ, δ, η with α + β + γ + δ + ... See full document

... connected graph of |G| vertices with G ...first graph G is connected by edges with those vertices which are adjacent to the corresponding vertex of the second graph G and the resultant graph is ... See full document

... A graph G with a specified vertex subset U V(G) is denoted by ...The generalized hierarchical product, denoted by G(U)H, is the graph with vertex set V(G) V(H) and two vertices (g, h) and (g′, h′) ... 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