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

2012 ◽  
Vol 11 (4) ◽  
pp. 121-131 ◽  
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.

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

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.

scholarly journals Some New Classes of Open Distance-Pattern Uniform Graphs

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Bibin K. Jose
Keyword(s):  
Nonempty Subset ◽  
Chordal Graphs ◽  
Outerplanar Graph ◽  
Outerplanar Graphs ◽  
Induced Subgraphs ◽  
Minimum Cardinality ◽  
Maximal Outerplanar Graphs ◽  
Split Graphs ◽  
Strongly Chordal Graphs

Given an arbitrary nonempty subset M of vertices in a graph G=(V,E), each vertex u in G is associated with the set fMo(u)={d(u,v):v∈M,u≠v} and called its open M-distance-pattern. The graph G is called open distance-pattern uniform (odpu-) graph if there exists a subset M of V(G) such that fMo(u)=fMo(v) for all u,v∈V(G), and M is called an open distance-pattern uniform (odpu-) set of G. The minimum cardinality of an odpu-set in G, if it exists, is called the odpu-number of G and is denoted by od(G). Given some property P, we establish characterization of odpu-graph with property P. In this paper, we characterize odpu-chordal graphs, and thereby characterize interval graphs, split graphs, strongly chordal graphs, maximal outerplanar graphs, and ptolemaic graphs that are odpu-graphs. We also characterize odpu-self-complementary graphs, odpu-distance-hereditary graphs, and odpu-cographs. We prove that the odpu-number of cographs is even and establish that any graph G can be embedded into a self-complementary odpu-graph H, such that G and G¯ are induced subgraphs of H. We also prove that the odpu-number of a maximal outerplanar graph is either 2 or 5.

scholarly journals Graphs with Constant Sum of Domination and Inverse Domination Numbers

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
T. Tamizh Chelvam ◽  
T. Asir
Keyword(s):  
Minimum Degree ◽  
Dominating Set ◽  
Domination Number ◽  
Complete Characterization ◽  
Dominating Sets ◽  
Minimum Cardinality ◽  
Connected Graphs ◽  
Vertex Set ◽  
Domination Numbers

A subset D of the vertex set of a graph G, is a dominating set if every vertex in V−D is adjacent to at least one vertex in D. The domination number γ(G) is the minimum cardinality of a dominating set of G. A subset of V−D, which is also a dominating set of G is called an inverse dominating set of G with respect to D. The inverse domination number γ′(G) is the minimum cardinality of the inverse dominating sets. Domke et al. (2004) characterized connected graphs G with γ(G)+γ′(G)=n, where n is the number of vertices in G. It is the purpose of this paper to give a complete characterization of graphs G with minimum degree at least two and γ(G)+γ′(G)=n−1.

Structural properties of super strongly perfect graphs

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.

scholarly journals A characterization of strongly chordal graphs

1998 ◽  
Vol 187 (1-3) ◽  
pp. 269-271 ◽  
Author(s):  
Elias Dahlhaus ◽  
Paul D. Manuel ◽  
Mirka Miller
Keyword(s):  
Chordal Graphs ◽  
Strongly Chordal Graphs

scholarly journals Algorithmic Aspects of Some Variations of Clique Transversal and Clique Independent Sets on Graphs

Algorithms ◽  
2021 ◽  
Vol 14 (1) ◽  
pp. 22
Author(s):  
Chuan-Min Lee
Keyword(s):  
Planar Graphs ◽  
Maximum Clique ◽  
Chordal Graphs ◽  
Perfect Graphs ◽  
Line Graphs ◽  
Np Completeness ◽  
Split Graphs ◽  
Transversal Numbers ◽  
The Relationship ◽  
Independence Numbers

This paper studies the maximum-clique independence problem and some variations of the clique transversal problem such as the {k}-clique, maximum-clique, minus clique, signed clique, and k-fold clique transversal problems from algorithmic aspects for k-trees, suns, planar graphs, doubly chordal graphs, clique perfect graphs, total graphs, split graphs, line graphs, and dually chordal graphs. We give equations to compute the {k}-clique, minus clique, signed clique, and k-fold clique transversal numbers for suns, and show that the {k}-clique transversal problem is polynomial-time solvable for graphs whose clique transversal numbers equal their clique independence numbers. We also show the relationship between the signed and generalization clique problems and present NP-completeness results for the considered problems on k-trees with unbounded k, planar graphs, doubly chordal graphs, total graphs, split graphs, line graphs, and dually chordal graphs.

scholarly journals Domination and Independent Domination in Hexagonal Systems

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 67
Author(s):  
Norah Almalki ◽  
Pawaton Kaemawichanurat
Keyword(s):  
Dominating Set ◽  
Domination Number ◽  
Free Graph ◽  
Hexagonal System ◽  
Induced Subgraph ◽  
Minimum Cardinality ◽  
Independent Domination ◽  
The Relationship ◽  
Hexagonal Systems ◽  
Domination Numbers

A vertex subset D of G is a dominating set if every vertex in V(G)∖D is adjacent to a vertex in D. A dominating set D is independent if G[D], the subgraph of G induced by D, contains no edge. The domination number γ(G) of a graph G is the minimum cardinality of a dominating set of G, and the independent domination number i(G) of G is the minimum cardinality of an independent dominating set of G. A classical work related to the relationship between γ(G) and i(G) of a graph G was established in 1978 by Allan and Laskar. They proved that every K1,3-free graph G satisfies γ(G)=i(H). Hexagonal systems (2 connected planar graphs whose interior faces are all hexagons) have been extensively studied as they are used to present bezenoid hydrocarbon structures which play an important role in organic chemistry. The domination numbers of hexagonal systems have been studied continuously since 2018 when Hutchinson et al. posted conjectures, generated from a computer program called Conjecturing, related to the domination numbers of hexagonal systems. Very recently in 2021, Bermudo et al. answered all of these conjectures. In this paper, we extend these studies by considering the relationship between the domination number and the independent domination number of hexagonal systems. Although every hexagonal system H with at least two hexagons contains K1,3 as an induced subgraph, we find many classes of hexagonal systems whose domination number is equal to an independent domination number. However, we establish the existence of a hexagonal system H such that γ(H)<i(H) with the prescribed number of hexagons.

Skeletal elements of crinoid echinoderms: High-resolution structural and microanalytical results

1983 ◽  
Vol 41 ◽  
pp. 194-195
Author(s):  
D. F. Blake ◽  
L. F. Allard ◽  
D. R. Peacor
Keyword(s):  
High Resolution ◽  
Marine Invertebrates ◽  
Sea Urchins ◽  
Structural Features ◽  
Sea Stars ◽  
High Resolution Tem ◽  
Relationship Of ◽  
The Relationship ◽  
Insight Into

Echinodermata is a phylum of marine invertebrates which has been extant since Cambrian time (c.a. 500 m.y. before the present). Modern examples of echinoderms include sea urchins, sea stars, and sea lilies (crinoids). The endoskeletons of echinoderms are composed of plates or ossicles (Fig. 1) which are with few exceptions, porous, single crystals of high-magnesian calcite. Despite their single crystal nature, fracture surfaces do not exhibit the near-perfect {10.4} cleavage characteristic of inorganic calcite. This paradoxical mix of biogenic and inorganic features has prompted much recent work on echinoderm skeletal crystallography. Furthermore, fossil echinoderm hard parts comprise a volumetrically significant portion of some marine limestones sequences. The ultrastructural and microchemical characterization of modern skeletal material should lend insight into: 1). The nature of the biogenic processes involved, for example, the relationship of Mg heterogeneity to morphological and structural features in modern echinoderm material, and 2). The nature of the diagenetic changes undergone by their ancient, fossilized counterparts. In this study, high resolution TEM (HRTEM), high voltage TEM (HVTEM), and STEM microanalysis are used to characterize tha ultrastructural and microchemical composition of skeletal elements of the modern crinoid Neocrinus blakei.

Microstructural Characterization of Au-Ge-Ni based ohmic contacts to GaAs/AlGaAs modfet device

1987 ◽  
Vol 45 ◽  
pp. 326-327
Author(s):  
A.K. Rai ◽  
A.K. Petford-Long ◽  
A. Ezis ◽  
D.W. Langer
Keyword(s):  
Contact Resistance ◽  
Ohmic Contact ◽  
Ohmic Contacts ◽  
Microstructural Characterization ◽  
Almost Everywhere ◽  
Spacer Layer ◽  
Good Contact ◽  
The Relationship ◽  
Lower Contact

Considerable amount of work has been done in studying the relationship between the contact resistance and the microstructure of the Au-Ge-Ni based ohmic contacts to n-GaAs. It has been found that the lower contact resistivity is due to the presence of Ge rich and Au free regions (good contact area) in contact with GaAs. Thus in order to obtain an ohmic contact with lower contact resistance one should obtain a uniformly alloyed region of good contact areas almost everywhere. This can possibly be accomplished by utilizing various alloying schemes. In this work microstructural characterization, employing TEM techniques, of the sequentially deposited Au-Ge-Ni based ohmic contact to the MODFET device is presented.The substrate used in the present work consists of 1 μm thick buffer layer of GaAs grown on a semi-insulating GaAs substrate followed by a 25 Å spacer layer of undoped AlGaAs.

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