A special k-coloring for a connected k-chromatic graph

Approximation Algorithms for k-Connected Graph Factors

Finding low-cost spanning subgraphs with given degree and connectivity requirements is a fundamental problem in the area of network design. We consider the problem of finding d-regular spanning subgraphs (or d-factors) of minimum weight with connectivity requirements. For the case of k-edge-connectedness, we present approximation algorithms that achieve constant approximation ratios for all d ≥...

Spectral Conditions for a Graph to be k-Connected

(k,r) - Semi Strong Chromatic Number of a Graph

Let G = (V, E) be a simple, finite, undirected graph. Let k, r be positive integers. A set S  V (G) is called (k, r)-semi strongly stable set if | (u) S|  k, for all u V (G). A partition of V(G) into (k, r)-semi strongly stable sets is called (k, r)-semi strong coloring of G. The minimum order of a (k, r)-semi strong coloring of G is called (k, r)-semi strong chromatic number of G and it is...

Some special minimum k-geodetically connected graphs

A connected graph G is k-geodetically connected (k-GC) if the removal of less than k vertices does not affect the distances (lengths of the shortest paths) between any pair of the remaining vertices. As such graphs have important applications in robust system designs, we are interested in theminimumnumber of edges required tomake a k-GC graph of order n, and characterizing those minimum k-GC gr...

A practical algorithm for [r, s, t]-coloring of graph

Coloring graphs is one of important and frequently used topics in diverse sciences. In the majority of the articles, it is intended to find a proper bound for vertex coloring, edge coloring or total coloring in the graph. Although it is important to find a proper algorithm for graph coloring, it is hard and time-consuming too. In this paper, a new algorithm for vertex coloring, edge coloring an...