the eccentricity connectivity index of a molecular graph g is defined as (g) = av(g)deg(a)ε(a), where ε(a) is defined as the length of a maximal path connecting a to othervertices of g and deg(a) is degree of vertex a. here, we compute this topological index forsome infinite classes of dendrimer graphs.

We investigate combinatorial and algebraic aspects of the interplay between renormalization monodromies for Feynman amplitudes. clarify how extraction subgraphs from a graph interacts with putting edges onshell or contracting them to obtain reduced graphs. Graph by this leads study cointeracting bialgebras. One bialgebra comes hence is needed renormalization. The other an incidence put either o...

solvable graphs (also known as reachable graphs) are types of graphs that any arrangement of a specified number of agents located on the graph’s vertices can be reached from any initial arrangement through agents’ moves along the graph’s edges, while avoiding deadlocks (interceptions). in this paper, the properties of solvable graphs are investigated, and a new concept in multi agent moti...

It is shown explicitly how self-similar graphs can be obtained as ‘blow-up’ constructions of finite cell graphs Ĉ. This yields a larger family of graphs than the graphs obtained by discretising continuous self-similar fractals. For a class of symmetrically self-similar graphs we study the simple random walk on a cell graph Ĉ, starting at a vertex v of the boundary of Ĉ. It is proved that the ex...

The tenacity of an incomplete connected graph G is defined as T (G) = min{ |S|+m(G−S) ω(G−S) : S ⊂ V (G), ω(G− S) > 1}, where ω(G− S) and m(G− S), respectively, denote the number of components and the order of a largest component inG−S. This is a reasonable parameter to measure the vulnerability of networks, as it takes into account both the amount of work done to damage the network and how bad...

Topoi are known to be categories with extra properties that make them much alike the category of Sets. In a Topoi it is possible to define adequate notions of membership, elements and subobjects, power ”sets”, and finally, every Topoi has an internal logic able to justify any reasoning carried inside it. Most of the cases, this logic is not Classical (Boolean). The general logic for the Topoi i...

Article history: Available online 25 March 2011 Submitted by J.J. Loiseau AMS classification: 15A80 15A39 15A03

distance-balanced graphs are introduced as graphs in which every edge uv has the followingproperty: the number of vertices closer to u than to v is equal to the number of vertices closerto v than to u. basic properties of these graphs are obtained. in this paper, we study theconditions under which some graph operations produce a distance-balanced graph.

a special class of cubic graphs are the cycle permutation graphs. a cycle permutation graph pn(α) is defined by taking two vertex-disjoint cycles on n vertices and adding a matching between the vertices of the two cycles.in this paper we determine a good upper bound for tenacity of cycle permutation graphs.

the total version of geometric–arithmetic index of graphs is introduced based on the endvertexdegrees of edges of their total graphs. in this paper, beside of computing the total gaindex for some graphs, its some properties especially lower and upper bounds are obtained.