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Topics in Chromatic Graph Theory: Colouring random graphs
, 2015How many colours are typically necessary to colour a graph? We survey a number of perspectives on this natural question, which is central to random graph theory and to probabilistic and extremal combinatorics. It has stimulated a vibrant area of research,
Ross J. Kang, C. McDiarmid
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Configurations of DNA cages based on plane graphs and vertex junctions
Journal of Physics A: Mathematical and Theoretical, 1965Surface wave phase velocities for an inhomogeneous medium are usually given as eigenvalues of the wave equation. This is a differential equation (Love waves) or pair of differential equations (Rayleigh waves) of the second order. By means of a change of variable the problem is reducible to finding the zeros of a first‐order differential equation or ...
M. G. Neigauz +2 more
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[Most frequent themes in Editorials of Vertex journal (1990-2019) analyzed by graph theory].
Vertex (Buenos Aires, Argentina), 2022The analysis of Editorials is a little explored topic, which can facilitate the understanding of historical processes and changes in Psychiatry. In the case of de Vertex Revista Argentina de Psiquiatría, the Editorials were written by the same person for 30 years. The most frequently used thematic areas were studied, using graph theory, to characterize
Daniel, Matusevich +3 more
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Graph Parameters and Ramsey Theory
International Workshop on Combinatorial Algorithms, 2016Ramsey’s Theorem tells us that there are exactly two minimal hereditary classes containing graphs with arbitrarily many vertices: the class of complete graphs and the class of edgeless graphs.
V. Lozin
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, 1992
INTRODUCTION. ELEMENTS OF GRAPH THEORY. The Definition of a Graph. Isomorphic Graphs and Graph Automorphism. Walks, Trails, Paths, Distances and Valencies in Graphs. Subgraphs. Regular Graphs. Trees. Planar Graphs.
N. Trinajstic
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INTRODUCTION. ELEMENTS OF GRAPH THEORY. The Definition of a Graph. Isomorphic Graphs and Graph Automorphism. Walks, Trails, Paths, Distances and Valencies in Graphs. Subgraphs. Regular Graphs. Trees. Planar Graphs.
N. Trinajstic
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On the Shannon capacity of a graph
IEEE Transactions on Information Theory, 1979It is proved that the Shannon zero-error capacity of the pentagon is \sqrt{5} . The method is then generalized to obtain upper bounds on the capacity of an arbitrary graph.
L. Lovász
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Iwasawa theory for vertex-weighted graphs
29 pages, 8 ...Murooka, Ryosuke, Tateno, Sohei
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A fuzzy irregular cellular automata-based method for the vertex colouring problem
Connection science, 2019Vertex colouring is among the most important problems in graph theory which has been widely applied across different real-world problems. In vertex colouring problem (VCP), the goal is to assign a distinct colour to each vertex of the graph in such a way
M. Kashani, S. Gorgin, S. V. Shojaedini
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Algebraic Graph Theory: COLOURING PROBLEMS
, 19741. Introduction to algebraic graph theory Part I. Linear Algebra in Graphic Thoery: 2. The spectrum of a graph 3. Regular graphs and line graphs 4. Cycles and cuts 5. Spanning trees and associated structures 6. The tree-number 7. Determinant expansions 8.
N. Biggs
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Application of molecular orbital graph theory——A cutting vertex method for evaluating E_π
, 1996 Simone Hu +5 more
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