in this paper, a new online robot motion planner is developed for systematically exploring unknown environâ¬ments by intelligent mobile robots in real-time applications. the algorithm takes advantage of sensory data to find an obstacle-free start-to-goal path. it does so by online calculation of the generalized voronoi graph (gvg) of the free space, and utilizing a combination of depth-first an...

the concept of the bipartite divisor graph for integer subsets has been considered in [‎graph combinator., ‎ 26 (2010) 95--105‎.]. ‎in this paper‎, ‎we will consider this graph for the set of character degrees of a finite group $g$ and obtain some properties of this graph‎. ‎we show that if $g$ is a solvable group‎, ‎then the number of connected components of this graph is at most $2$ and if $g...

In a signed graph G, a negative clique is a complete subgraph having negative edges only. In this article, we give characteristic polynomial expressions, and eigenvalues of some signed graphs having negative cliques. This includes signed cycle graph, signed path graph, a complete graph with disjoint negative cliques, and star block graph with negative cliques.

in this paper we construct antimagic labelings of the regular complete multipartite graphs and we also extend the construction to some families of regular graphs.

A path in an edge-colored graph is said to be a rainbow path if no two edges on the path have the same color. An edge-colored graph is (strongly) rainbow connected if there exists a rainbow (geodesic) path between every pair of vertices. The (strong) rainbow connection number of G, denoted by (scr(G), respectively) rc(G), is the smallest number of colors that are needed in order to make G (stro...

Let G denote a graph, and KV(G) represent a set of target vertices. Assume that the non-target vertices of G fail independently with given probabilities. The K-terminal reliability of G is defined as the probability that all target vertices in K are connected. Computing K-terminal reliability is #P-complete for general graphs, yet solvable in polynomial time for interval graphs. This work prop...

We present two space-efficient algorithms. First, we show how to report a simple path between two arbitrary nodes in a given tree. Using a technique called “computing instead of storing”, we can design a naive quadratic-time algorithm for the problem using only constant work space, i.e., O(log n) bits in total for the work space, where n is the number of nodes in the tree. Then, another techniq...

k-Interval Routing Scheme (k-IRS) is a compact routing method that allows up to k interval labels to be assigned to an arc; and global k-IRS allows not more than a total of k interval labels in the whole network. A fundamental problem is to characterize the networks that admit k-IRS (or global k-IRS). Many of the problems related to single-shortest-path k-IRS have already been shown to be NP-co...

In this note, we show that some problems related to the length of the longest simple path from a given vertex in a graph are NP-complete. We also discuss an extension to the graph coloring problem. @ 2004 Elsevier Ltd. All rights reserved. Keywords-Longest path, Graph coloring, Complexity.

The Minimum Eccentricity Shortest Path Problem consists in finding a shortest path with minimum eccentricity given undirected graph. problem is known to be NP-complete and W[2]-hard respect the desired eccentricity. We present fpt-algorithms for parameterized by modular width, distance cluster graph, combination of treewidth eccentricity, maximum leaf number.