WebAug 28, 2008 · A set S of vertices in a graph G is a total dominating set, denoted by TDS, of G if every vertex of G is adjacent to some vertex in S (other than itself). The minimum cardinality of a TDS of G is the total domination number of G, denoted by γ t (G).If G does not contain K 1, 3 as an induced subgraph, then G is said to be claw-free. It is shown in … WebJul 10, 2015 · The cyclability of a graph H, denoted by C(H), is the largest integer r such that H has a cycle through any r vertices. For a claw-free graph H, by Ryjáček (J Comb …
graph theory - Prove that all linegraphs L(G) are claw free ...
WebA line graph L(G) (also called an adjoint, conjugate, covering, derivative, derived, edge, edge-to-vertex dual, interchange, representative, or theta-obrazom graph) of a simple … A claw-free graph is a graph in which no induced subgraph is a claw; i.e., any subset of four vertices has other than only three edges connecting them in this pattern. Equivalently, a claw-free graph is a graph in which the neighborhood of any vertex is the complement of a triangle-free graph. See more 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 K1,3 (that is, a star graph comprising three … See more Because claw-free graphs include complements of triangle-free graphs, the number of claw-free graphs on n vertices grows at least as quickly as the number of triangle-free … See more An independent set in a line graph corresponds to a matching in its underlying graph, a set of edges no two of which share an endpoint. The blossom algorithm of Edmonds (1965) finds a maximum matching in any graph in polynomial time, … See more • The line graph L(G) of any graph G is claw-free; L(G) has a vertex for every edge of G, and vertices are adjacent in L(G) whenever the … See more It is straightforward to verify that a given graph with n vertices and m edges is claw-free in time O(n ), by testing each 4-tuple of vertices to determine whether they induce a claw. With … See more Sumner (1974) and, independently, Las Vergnas (1975) proved that every claw-free connected graph with an even number of vertices has a perfect matching. That is, there exists a set of edges in the graph such that each vertex is an endpoint of exactly one of the … See more A perfect graph is a graph in which the chromatic number and the size of the maximum clique are equal, and in which this equality … See more nothing\\u0027s news clint black lyrics
Closure concepts for claw-free graphs - ScienceDirect
WebMay 19, 2000 · The claw is the complete bipartite graph K 1, 3 . The class of claw-free graphs is widely studied in a variety of contexts and has a vast literature; see [10] for a survey. A detailed and complete ... WebMar 6, 2024 · 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 … WebAlgebraic graph theory is a branch of mathematics in which algebraic methods are applied to problems about graphs. This is in contrast to geometric, combinatoric, or algorithmic approaches. There are three main branches of algebraic graph theory, involving the use of linear algebra, the use of group theory, and the study of graph invariants . how to set up twitch about me