The edge clique cover sum number (resp. edge clique partition sum number) of a graph G, denoted by scc(G) (resp. scp(G)), is defined as the smallest integer k for which there exists a collection of complete subgraphs of G, covering (resp. partitioning) all edges of G such that the sum of sizes of the cliques is at most k. By definition, scc(G) 5 scp(G). Also, it is known that for every graph G ...

We show that every outerplanar graph can be linearly embedded in the plane such number of distinct distances between pairs adjacent vertices is at most thirteen and there no intersection image a vertex an edge not containing it.

A robust and eecient algorithm for discretization of tensor product polynomial surfaces is presented. The advancing front technique operating directly on the surface in the physical space is employed. This avoids diiculties with the anisotropic trian-gulation of parametric space of these surfaces and also guarantees the creation of well shaped triangles even in case of degenerated or badly para...

An edge reconnection is an operation on a path of three consecutive vertices (a, b, c) of a chain or tree linkage; refer to Figure 1. If it is possible to fold the linkage, preserving edge lengths and avoiding self-intersection, to bring the two incident edges ab and bc into coincidence, then the edge reconnection breaks the connection between the edges at b, splits b into two vertices b1 and b...

In this paper, we study sequences of regressions in joint or single responses given a set of context variables, where a dependence structure of interest is captured by a regression graph. These graphs have nodes representing random variables and three types of edge. Their set of missing edges defines the independence structure of the graph provided two properties are used that are not common to...

, for t ∈ R. (1) The line lab is the set of parameterizations of the rotations of R 2 that take a to b. We consider the set of n lines L = {lab : a, b ∈ P}. (2) To prove that P determines Ω(n/ log n) distinct distances, it suffices to prove that the number of pairs of intersecting lines in L is O(n logn). Let Nk denote the number of points in R that are incident to exactly k lines of L, and let...

In 1994 S. McGuinness showed that any greedy clique decomposition of an n-vertex graph has at most ⌊n2/4⌋ cliques (The greedy clique decomposition of a graph, J. Graph Theory 18 (1994) 427-430), where a clique decomposition means a clique partition of the edge set and a greedy clique decomposition of a graph is obtained by removing maximal cliques from a graph one by one until the graph is empt...

Random key graphs have originally been introduced in the context of a random key predistribution scheme for securing wireless sensor networks (WSNs). Since then, they have appeared in applications spanning recommender systems, social networks, clustering and classification analysis, and cryptanalysis of hash functions. Random key graphs, denoted G(n;K,P ), form a class of random intersection gr...

Roundabout is one of the most effective intersection control methods in the world. Although, they have often been used in Iran, but, the methods which are proposed to analyze roundabouts are very old and new regulations are not implemented for analyzing modern roundabouts. There are strong needs to apply new modern analyzing methods for studying roundabouts in Iran. Also, these methods should b...