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Strong Product Of Graphs
In graph theory, the strong product is a way of combining two graphs to make a larger graph. Two vertices are adjacent in the strong product when they come from pairs of vertices in the factor graphs that are either adjacent or identical. The strong product is one of several different graph product operations that have been studied in graph theory. The strong product of any two graphs can be constructed as the union of two other products of the same two graphs, the Cartesian product of graphs and the tensor product of graphs. An example of a strong product is the king's graph, the graph of moves of a chess king on a chessboard, which can be constructed as a strong product of path graphs. Decompositions of planar graphs and related graph classes into strong products have been used as a central tool to prove many other results about these graphs. Care should be exercised when encountering the term ''strong product'' in the literature, since it has also been used to denote the tenso ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
King's Graph
In graph theory, a king's graph is a graph that represents all legal moves of the king chess piece on a chessboard where each vertex represents a square on a chessboard and each edge is a legal move. More specifically, an n \times m king's graph is a king's graph of an n \times m chessboard. It is the map graph formed from the squares of a chessboard by making a vertex for each square and an edge for each two squares that share an edge or a corner. It can also be constructed as the strong product of two path graphs. For an n \times m king's graph the total number of vertices is n m and the number of edges is 4nm -3(n + m) + 2. For a square n \times n king's graph this simplifies so that the total number of vertices is n^2 and the total number of edges is (2n-2)(2n-1). The neighbourhood of a vertex in the king's graph corresponds to the Moore neighborhood for cellular automata. A generalization of the king's graph, called a kinggraph, is formed from a squaregraph (a planar graph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Queue Number
In the mathematical field of graph theory, the queue number of a graph is a graph invariant defined analogously to stack number (book thickness) using first-in first-out (queue) orderings in place of last-in first-out (stack) orderings. Definition A queue layout of a given graph is defined by a total ordering of the vertices of the graph together with a partition of the edges into a number of "queues". The set of edges in each queue is required to avoid edges that are properly nested: if and are two edges in the same queue, then it should not be possible to have in the vertex ordering. The queue number of a graph is the minimum number of queues in a queue layout.. Equivalently, from a queue layout, one could process the edges in a single queue using a queue data structure, by considering the vertices in their given ordering, and when reaching a vertex, dequeueing all edges for which it is the second endpoint followed by enqueueing all edges for which it is the first en ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Twin-width
The twin-width of an undirected graph is a natural number associated with the graph, used to study the parameterized complexity of graph algorithms. Intuitively, it measures how similar the graph is to a cograph, a type of graph that can be reduced to a single vertex by repeatedly merging together ''twins'', vertices that have the same neighbors. The twin-width is defined from a sequence of repeated mergers where the vertices are not required to be twins, but have nearly equal sets of neighbors. Definition Twin-width is defined for finite simple undirected graphs. These have a finite set of vertices, and a set of edges that are unordered pairs of vertices. The open neighborhood of any vertex is the set of other vertices that it is paired with in edges of the graph; the closed neighborhood is formed from the open neighborhood by including the vertex itself. Two vertices are ''true twins'' when they have the same closed neighborhood, and ''false twins'' when they have the same open ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrete Applied Mathematics
''Discrete Applied Mathematics'' is a peer-reviewed scientific journal covering algorithmic and applied areas of discrete mathematics. It is published by Elsevier and the editor-in-chief is Endre Boros (Rutgers University). The journal was split off from another Elsevier journal, ''Discrete Mathematics'', in 1979, with that journal's founder Peter Ladislaw Hammer as its founding editor-in-chief. Abstracting and indexing The journal is abstracted and indexing in: According to the ''Journal Citation Reports'', the journal has a 2020 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a scientometric index calculated by Clarivate that reflects the yearly mean number of citations of articles published in the last two years in a given journal, as i ... of 1.139. References External links *{{official website, http://www.journals.elsevier.com/discrete-applied-mathematics/ Combinatorics journals Publications established in 1979 Englis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clique Number
In the mathematical area of graph theory, a clique ( or ) is a subset of vertices of an undirected graph such that every two distinct vertices in the clique are adjacent. That is, a clique of a graph G is an induced subgraph of G that is complete. Cliques are one of the basic concepts of graph theory and are used in many other mathematical problems and constructions on graphs. Cliques have also been studied in computer science: the task of finding whether there is a clique of a given size in a graph (the clique problem) is NP-complete, but despite this hardness result, many algorithms for finding cliques have been studied. Although the study of complete subgraphs goes back at least to the graph-theoretic reformulation of Ramsey theory by , the term ''clique'' comes from , who used complete subgraphs in social networks to model cliques of people; that is, groups of people all of whom know each other. Cliques have many other applications in the sciences and particularly in bioinf ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1-planar Graph
In topological graph theory, a 1-planar graph is a graph that can be drawn in the Euclidean plane in such a way that each edge has at most one crossing point, where it crosses a single additional edge. If a 1-planar graph, one of the most natural generalizations of planar graphs, is drawn that way, the drawing is called a 1-plane graph or 1-planar embedding of the graph. Coloring 1-planar graphs were first studied by , who showed that they can be colored with at most seven colors. Later, the precise number of colors needed to color these graphs, in the worst case, was shown to be six.. The example of the complete graph ''K''6, which is 1-planar, shows that 1-planar graphs may sometimes require six colors. However, the proof that six colors are always enough is more complicated. Ringel's motivation was in trying to solve a variation of total coloring for planar graphs, in which one simultaneously colors the vertices and faces of a planar graph in such a way that no two adjacent ve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinatorics, Probability And Computing
''Combinatorics, Probability and Computing'' is a peer-reviewed scientific journal in mathematics published by Cambridge University Press. Its editor-in-chief is Béla Bollobás (DPMMS and University of Memphis). History The journal was established by Bollobás in 1992. Fields Medalist Timothy Gowers calls it "a personal favourite" among combinatorics journals and writes that it "maintains a high standard". Content The journal covers combinatorics, probability theory, and theoretical computer science. Currently, it publishes six issues annually. As with other journals from the same publisher, it follows a hybrid green/gold open access policy, in which authors may either place copies of their papers in an institutional repository after a six-month embargo period, or pay an open access charge to make their papers free to read on the journal's website. Abstracting and indexing The journal is abstracted and indexed in: According to the ''Journal Citation Reports'', the jou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Apex Graph
In graph theory, a branch of mathematics, an apex graph is a graph that can be made planar by the removal of a single vertex. The deleted vertex is called an apex of the graph. It is ''an'' apex, not ''the'' apex because an apex graph may have more than one apex; for example, in the minimal nonplanar graphs or , every vertex is an apex. The apex graphs include graphs that are themselves planar, in which case again every vertex is an apex. The null graph is also counted as an apex graph even though it has no vertex to remove. Apex graphs are closed under the operation of taking minors and play a role in several other aspects of graph minor theory: linkless embedding, Hadwiger's conjecture,. YΔY-reducible graphs, and relations between treewidth and graph diameter. Characterization and recognition Apex graphs are closed under the operation of taking minors: contracting any edge, or removing any edge or vertex, leads to another apex graph. For, if is an apex graph with apex , ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Forbidden Graph Characterization
In graph theory, a branch of mathematics, many important families of graphs can be described by a finite set of individual graphs that do not belong to the family and further exclude all graphs from the family which contain any of these forbidden graphs as (induced) subgraph or minor. A prototypical example of this phenomenon is Kuratowski's theorem, which states that a graph is planar (can be drawn without crossings in the plane) if and only if it does not contain either of two forbidden graphs, the complete graph and the complete bipartite graph . For Kuratowski's theorem, the notion of containment is that of graph homeomorphism, in which a subdivision of one graph appears as a subgraph of the other. Thus, every graph either has a planar drawing (in which case it belongs to the family of planar graphs) or it has a subdivision of at least one of these two graphs as a subgraph (in which case it does not belong to the planar graphs). Definition More generally, a forbidden grap ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrete Mathematics & Theoretical Computer Science
''Discrete Mathematics & Theoretical Computer Science'' is a peer-reviewed open access scientific journal covering discrete mathematics and theoretical computer science. It was established in 1997 by Daniel Krob (Paris Diderot University). Since 2001, the editor-in-chief is Jens Gustedt (Institut National de Recherche en Informatique et en Automatique). Abstracting and indexing The journal is abstracted and indexed in ''Mathematical Reviews'' and the Science Citation Index Expanded. According to the ''Journal Citation Reports'', the journal has a 2011 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a scientometric index calculated by Clarivate that reflects the yearly mean number of citations of articles published in the last two years in a given journal, as i ... of 0.465. References External links * {{DEFAULTSORT:Discrete Mathematics and Theoretical Computer Science Combinatorics journals Computer science journals Pub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph Embedding
In topological graph theory, an embedding (also spelled imbedding) of a Graph (discrete mathematics), graph G on a surface (mathematics), surface \Sigma is a representation of G on \Sigma in which points of \Sigma are associated with graph theory, vertices and simple arcs (Homeomorphism, homeomorphic images of [0,1]) are associated with graph theory, edges in such a way that: * the endpoints of the arc associated with an edge e are the points associated with the end vertices of e, * no arcs include points associated with other vertices, * two arcs never intersect at a point which is interior to either of the arcs. Here a surface is a compact space, compact, connected space, connected 2-manifold. Informally, an embedding of a graph into a surface is a drawing of the graph on the surface in such a way that its edges may intersect only at their endpoints. It is well known that any finite graph can be embedded in 3-dimensional Euclidean space \mathbb^3.. A planar graph is one that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithmica
''Algorithmica'' received the highest possible ranking “A*”. External links Springer information Computer science journals Springer Science+Business Media academic journals Monthly journals Publications established in 1986 English-language journals ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
