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In graph theory, a star S k is the complete bipartite graph K 1,k : a tree with one internal node and k leaves (but no internal nodes and k + 1 leaves when k ≤ 1). Alternatively, some authors define S k to be the tree of order k with maximum diameter 2; in which case a star of k > 2 has k − 1 leaves. A star with 3 edges is called a claw.
Graph homomorphism problem [3]: GT52 Graph partition into subgraphs of specific types (triangles, isomorphic subgraphs, Hamiltonian subgraphs, forests, perfect matchings) are known NP-complete. Partition into cliques is the same problem as coloring the complement of the given graph. A related problem is to find a partition that is optimal terms ...
Example of a Ring Star Problem network. The ring star problem (RSP) is a NP-hard problem [1] in combinatorial optimization.In a complete weighted mixed graph, the ring star problem aims to find a minimum cost ring star subgraph formed by a cycle (ring part) and a set of arcs (star part) such that each arc's child node belongs to the cycle and each arc's parent node does not.
A complete bipartite graph of K 4,7 showing that Turán's brick factory problem with 4 storage sites (yellow spots) and 7 kilns (blue spots) requires 18 crossings (red dots) For any k, K 1,k is called a star. [2] All complete bipartite graphs which are trees are stars. The graph K 1,3 is called a claw, and is used to define the claw-free graphs ...
The Subgraph Isomorphism problem is NP-complete. The graph isomorphism problem is suspected to be neither in P nor NP-complete, though it is in NP. This is an example of a problem that is thought to be hard, but is not thought to be NP-complete. This class is called NP-Intermediate problems and exists if and only if P≠NP.
A* (pronounced "A-star") is a graph traversal and pathfinding algorithm that is used in many fields of computer science due to its completeness, optimality, and optimal efficiency. [1] Given a weighted graph , a source node and a goal node, the algorithm finds the shortest path (with respect to the given weights) from source to goal.
If, for example, there are two balls and three bins, then the number of ways of placing the balls is (+) = =. The table shows the six possible ways of distributing the two balls, the strings of stars and bars that represent them (with stars indicating balls and bars separating bins from one another), and the subsets that correspond to the strings.
Every quotient graph has one of three forms: it may be a prime graph, a complete graph, or a star. [2] A graph may have exponentially many different splits, but they are all represented in the split decomposition tree, either as an edge of the tree (for a strong split) or as an arbitrary partition of a complete or star quotient graph (for a ...