Structural properties of super strongly perfect graphs

A graph [Formula: see text] is super strongly perfect if every induced subgraph [Formula: see text] of [Formula: see text] possesses a minimal dominating set meeting all the maximal cliques of [Formula: see text]. Different structural properties of super strongly perfect graphs are studied in this paper. Some of the special categories of super strongly perfect graphs are identified and characterized. Certain operations of super strongly perfect graphs are also discussed towards the end.

Self-Stabilizing Algorithm for Minimal Dominating Set with Safe Convergence in an Arbitrary Graph

In a graph or a network [Formula: see text], a set [Formula: see text] is a dominating set if each node in [Formula: see text] is adjacent to at least one node in [Formula: see text]. A dominating set [Formula: see text] is called minimal when there does not exist a node [Formula: see text] such that the set [Formula: see text] is a dominating set. In this paper, we propose a new self-stabilizing algorithm for minimal dominating set. It has safe convergence property under synchronous daemon in the sense that starting from an arbitrary state, it quickly converges to a dominating set (a safe state) in two rounds, and then stabilizes in a minimal dominating set (the legitimate state) in [Formula: see text] rounds without breaking safety during the convergence interval, where n is the number of nodes. Space requirement at each node is [Formula: see text] bits.

Applications of Super Strongly Perfect Graph for Manufacturing System towards a Leaner Structure

Some restructuring decisions are conceptualized which reflect the aim of the organization to gradually evolve the manufacturing system towards a leaner structure. This is done by way of defining simplified process so that lesser hindrance in terms of cycles of interactions is found. The reframing decisions are given by five restructured configurations of the manufacturing system. Models using graph theory are developed for original configuration and each of the new reframed configurations and the resulting structural characterization information is used to compare the structure of restructured configurations with the original configuration. A graph G is Super Strongly Perfect (SSP) if every induced sub graph H of G possesses a minimal dominating set that meets all the maximal cliques of H. A study on some classes of super strongly perfect graphs like wheel and double wheel graphs (in which each graph represents structure of some manufacturing system) are given.