87 research outputs found

    Labeling, Covering and Decomposing of Graphs — Smarandache's Notion in Graph Theory

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    This paper surveys the applications of Smarandache’s notion to graph theory appeared in International J.Math.Combin. from Vol.1,2008 to Vol.3,2009. In fact, many problems discussed in these papers are generalized in this paper

    A partial prehistory of the Southwest Silk Road: Archaeometallurgical networks along the sub-Himalayan corridor

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    Historical phenomena often have prehistoric precedents, with this paper we investigate the potential for archaeometallurgical analyses and networked data processing to elucidate the progenitors of the Southwest Silk Road in Mainland Southeast Asia and southern China. We present original microstructural, elemental and lead isotope data for 40 archaeological copperbase metal samples, mostly from the UNESCO-listed site of Halin, and lead isotope data for 25 geological copper-mineral samples, also from Myanmar. We combined these data with existing datasets (N=98 total) and compared them to the 1000+ sample late prehistoric archaeometallurgical database available from Cambodia, Laos, Thailand, Vietnam and Yunnan. Lead isotope data, contextualised for alloy, find location and date, were interpreted manually for intra-site, inter-site and inter-regional consistency, which hint at significant multi-scalar connectivity from the late 2nd millennium BC. To test this interpretation statistically, the archaeological lead isotope data were then processed using regionally-adapted productionderived consistency parameters. Complex networks analysis using the Leiden community detection algorithm established groups of artefacts sharing lead isotopic consistency. Introducing the geographic component allowed for the identification of communities of sites with consistent assemblages. The four major communities were consistent with the manually interpreted exchange networks and suggest southern sections of the Southwest Silk Road were active in the late 2nd millennium BC

    On b-colorings and b-continuity of graphs

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    A b-coloring of G is a proper vertex coloring such that there is a vertex in each color class, which is adjacent to at least one vertex in every other color class. Such a vertex is called a color-dominating vertex. The b-chromatic number of G is the largest k such that there is a b-coloring of G by k colors. Moreover, if for every integer k, between chromatic number and b-chromatic number, there exists a b-coloring of G by k colors, then G is b-continuous. Determining the b-chromatic number of a graph G and the decision whether the given graph G is b-continuous or not is NP-hard. Therefore, it is interesting to find new results on b-colorings and b-continuity for special graphs. In this thesis, for several graph classes some exact values as well as bounds of the b-chromatic number were ascertained. Among all we considered graphs whose independence number, clique number, or minimum degree is close to its order as well as bipartite graphs. The investigation of bipartite graphs was based on considering of the so-called bicomplement which is used to determine the b-chromatic number of special bipartite graphs, in particular those whose bicomplement has a simple structure. Then we studied some graphs whose b-chromatic number is close to its t-degree. At last, the b-continuity of some graphs is studied, for example, for graphs whose b-chromatic number was already established in this thesis. In particular, we could prove that Halin graphs are b-continuous.:Contents 1 Introduction 2 Preliminaries 2.1 Basic terminology 2.2 Colorings of graphs 2.2.1 Vertex colorings 2.2.2 a-colorings 3 b-colorings 3.1 General bounds on the b-chromatic number 3.2 Exact values of the b-chromatic number for special graphs 3.2.1 Graphs with maximum degree at most 2 3.2.2 Graphs with independence number close to its order 3.2.3 Graphs with minimum degree close to its order 3.2.4 Graphs G with independence number plus clique number at most number of vertices 3.2.5 Further known results for special graphs 3.3 Bipartite graphs 3.3.1 General bounds on the b-chromatic number for bipartite graphs 3.3.2 The bicomplement 3.3.3 Bicomplements with simple structure 3.4 Graphs with b-chromatic number close to its t-degree 3.4.1 Regular graphs 3.4.2 Trees and Cacti 3.4.3 Halin graphs 4 b-continuity 4.1 b-spectrum of special graphs 4.2 b-continuous graph classes 4.2.1 Known b-continuous graph classes 4.2.2 Halin graphs 4.3 Further graph properties concerning b-colorings 4.3.1 b-monotonicity 4.3.2 b-perfectness 5 Conclusion Bibliograph

    International Journal of Mathematical Combinatorics, Vol.3

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    The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly comprising 460 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences

    Practical algorithms for MSO model-checking on tree-decomposable graphs

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    Maximum K-vertex covers for some classes of graphs.

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    Leung Chi Wai.Thesis (M.Phil.)--Chinese University of Hong Kong, 2005.Includes bibliographical references (leaves 52-57).Abstracts in English and Chinese.Abstract --- p.iAcknowledgement --- p.iiiChapter 1 --- Introduction --- p.1Chapter 1.1 --- Motivations --- p.1Chapter 1.2 --- Related work --- p.3Chapter 1.2.1 --- Fixed-parameter tractability --- p.3Chapter 1.2.2 --- Maximum k-vertex cover --- p.4Chapter 1.2.3 --- Dominating set --- p.4Chapter 1.3 --- Overview of the thesis --- p.5Chapter 2 --- Preliminaries --- p.6Chapter 2.1 --- Notation and definitions --- p.6Chapter 2.1.1 --- Basic definitions --- p.6Chapter 2.1.2 --- Partial t-trees --- p.7Chapter 2.1.3 --- Cographs --- p.9Chapter 2.1.4 --- Chordal graphs and interval graphs --- p.11Chapter 2.2 --- Upper bound --- p.12Chapter 2.3 --- Extension method --- p.14Chapter 3 --- Planar Graphs --- p.17Chapter 3.1 --- Trees --- p.17Chapter 3.2 --- Partial t-trees --- p.23Chapter 3.3 --- Planar graphs --- p.30Chapter 4 --- Perfect Graphs --- p.34Chapter 4.1 --- Maximum k-vertex cover in cographs --- p.34Chapter 4.2 --- Maximum dominating k-set in interval graphs --- p.39Chapter 4.3 --- Maximum k-vertex subgraph in chordal graphs --- p.46Chapter 4.3.1 --- Maximum k-vertex subgraph in partial t- trees --- p.46Chapter 4.3.2 --- Maximum k-vertex subgraph in chordal graphs --- p.47Chapter 5 --- Concluding Remarks --- p.49Chapter 5.1 --- Summary of results --- p.49Chapter 5.2 --- Open problems --- p.5

    Combinatorial Structures in Hypercubes

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