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

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.766-767.943 ◽

2015 ◽

Vol 766-767 ◽

pp. 943-948

Author(s):

R. Mary Jeya Jothi

Keyword(s):

Graph Theory ◽

Structural Characterization ◽

Manufacturing System ◽

Dominating Set ◽

Perfect Graphs ◽

Perfect Graph ◽

System Models ◽

Wheel Graphs ◽

Minimal Dominating Set ◽

Original Configuration

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.

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Characterization of Super Strongly Perfect Graphs in Chordal and Strongly Chordal Graphs

Mapana Journal of Sciences ◽

10.12723/mjs.23.10 ◽

2012 ◽

Vol 11 (4) ◽

pp. 121-131 ◽

Cited By ~ 1

Author(s):

R Mary Jeya Jothi ◽

A Amutha

Keyword(s):

Dominating Set ◽

Chordal Graphs ◽

Perfect Graphs ◽

Perfect Graph ◽

Strongly Chordal Graphs ◽

Minimal Dominating Set ◽

The Relationship ◽

Odd Cycles ◽

Domination Numbers

A Graph G is Super Strongly Perfect Graph if every induced sub graph H of G possesses a minimal dominating set that meets all the maximal complete sub graphs of H. In this paper, we have investigated the characterization of Super Strongly Perfect graphs using odd cycles. We have given the characterization of Super Strongly Perfect graphs in chordal and strongly chordal graphs. We have presented the results of Chordal graphs in terms of domination and co - domination numbers γ and . We have given the relationship between diameter, domination and co - domination numbers of chordal graphs. Also we have analysed the structure of Super Strongly Perfect Graph in Chordal graphs and Strongly Chordal graphs.

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Structural properties of super strongly perfect graphs

Discrete Mathematics Algorithms and Applications ◽

10.1142/s1793830918500532 ◽

2018 ◽

Vol 10 (04) ◽

pp. 1850053

Author(s):

T. E. Soorya ◽

Sunil Mathew

Keyword(s):

Structural Properties ◽

Dominating Set ◽

Perfect Graphs ◽

Induced Subgraph ◽

Minimal Dominating Set

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.

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Connectivity of Semiring Valued Graphs

Symmetry ◽

10.3390/sym13071227 ◽

2021 ◽

Vol 13 (7) ◽

pp. 1227

Author(s):

Shyam Sundar Santra ◽

Prabhakaran Victor ◽

Mahadevan Chandramouleeswaran ◽

Rami Ahmad El-Nabulsi ◽

Khaled Mohamed Khedher ◽

...

Keyword(s):

Graph Theory ◽

Transportation Network ◽

Dominating Set ◽

Network Routing ◽

Graph Connectivity ◽

Edge Dominating Set

Graph connectivity theory is important in network implementations, transportation, network routing and network tolerance, among other things. Separation edges and vertices refer to single points of failure in a network, and so they are often sought-after. Chandramouleeswaran et al. introduced the principle of semiring valued graphs, also known as S-valued symmetry graphs, in 2015. Since then, works on S-valued symmetry graphs such as vertex dominating set, edge dominating set, regularity, etc. have been done. However, the connectivity of S-valued graphs has not been studied. Motivated by this, in this paper, the concept of connectivity in S-valued graphs has been studied. We have introduced the term vertex S-connectivity and edge S-connectivity and arrived some results for connectivity of a complete S-valued symmetry graph, S-path and S-star. Unlike the graph theory, we have observed that the inequality for connectivity κ(G)≤κ′(G)≤δ(G) holds in the case of S-valued graphs only when there is a symmetry of the graph as seen in Examples 3–5.

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