This paper describes and studies generalizations of the well known double ring network structures. Two classes of structures are studied, the N2R(p; q) and N2R(p; q; r) structures, of which the former is a special case of the well known Generalized Petersen Graphs. Basic properties of these structures are shown, indicating that they form a suitable base for future access network infrastructures...

An antimagic labeling of a finite simple undirected graph with q edges is a bijection from the set of edges to the set of integers {1, 2, · · · , q} such that the vertex sums are pairwise distinct, where the vertex sum at vertex u is the sum of labels of all edges incident to such vertex. A graph is called antimagic if it admits an antimagic labeling. It was conjectured by N. Hartsfield and G. ...

Menger's Theorem states that in a 3-connected graph, any two vertices are joined by three openly disjoint paths. Here we consider 3-connected cubic graphs where two vertices exist so that the three disjoint paths between them contain all of the vertices of the graph (we call these graphs 3*connected); and also where the latter is true for ALL pairs of vertices (globally 3*-connected). A necessa...

Abstract By suitably adjusting the tropical algebra technique we compute rainbow independent domination numbers of several infinite families graphs including Cartesian products $$C_n \Box P_m$$ C n ? P m </mm...

There are several graphs H for which the precise structure of graphs that do not contain a minor isomorphic to H is known. In particular, such structure theorems are known for K5 [13], V8 [8] and [7], the cube [3], the octahedron [4], and several others. Such characterizations can often be very useful, e.g., Hadwiger’s conjecture for k = 4 is verified by using the structure for K5-free graphs, ...

In this paper we consider a fundamental problem in the area of viral marketing, called TARGET SET SELECTION problem. In a a viral marketing setting, social networks are modeled by graphs with potential customers of a new product as vertices and friend relationships as edges, where each vertex v is assigned a threshold value θ(v). The thresholds represent the different latent tendencies of custo...

‎The excessive index of a bridgeless cubic graph $G$ is the least integer $k$‎, ‎such that $G$ can be covered by $k$ perfect matchings‎. ‎An equivalent form of Fulkerson conjecture (due to Berge) is that every bridgeless‎ ‎cubic graph has excessive index at most five‎. ‎Clearly‎, ‎Petersen graph is a cyclically 4-edge-connected snark with excessive index at least 5‎, ‎so Fouquet and Vanherpe as...