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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.
The star chromatic number of Dyck graph is 4, while the chromatic number is 2. In the mathematical field of graph theory, a star coloring of a graph G is a (proper) vertex coloring in which every path on four vertices uses at least three distinct colors.
In graph theory, an area of mathematics, a claw-free graph is a graph that does not have a claw as an induced subgraph. A claw is another name for the complete bipartite graph K 1 , 3 {\displaystyle K_{1,3}} (that is, a star graph comprising three edges, three leaves, and a central vertex).
In the area of mathematics known as graph theory, a tree is said to be starlike if it has exactly one vertex of degree greater than 2. This high-degree vertex is the root and a starlike tree is obtained by attaching at least three linear graphs to this central vertex.
In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints. In its simplest form, it is a way of coloring the vertices of a graph such that no two adjacent vertices are of the same color; this is called a vertex coloring .
3. In the theory of splits, cuts whose cut-set is a complete bipartite graph, a prime graph is a graph without any splits. Every quotient graph of a maximal decomposition by splits is a prime graph, a star, or a complete graph. 4. A prime graph for the Cartesian product of graphs is a connected graph that is not itself a product. Every ...
In the mathematical field of graph theory, the double-star snark is a snark with 30 vertices and 45 edges. [1]In 1975, Rufus Isaacs introduced two infinite families of snarks—the flower snark and the BDS snark, a family that includes the two Blanuša snarks, the Descartes snark and the Szekeres snark (BDS stands for Blanuša Descartes Szekeres). [2]
The Petersen graph is the smallest snark. The flower snark J 5 is one of six snarks on 20 vertices.. In the mathematical field of graph theory, a snark is an undirected graph with exactly three edges per vertex whose edges cannot be colored with only three colors.