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  1. 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 .

  2. 03/08/2022 · The line graph of any graph is claw-free, as is the complement of any triangle-free graph . Classes of graphs that are claw-free include 1. antiprism graphs, 2. barbell graphs, 3. bishop graphs (and their connected components), 4. cocktail party graphs , 5. complete graphs, 6. cycle graphs, 7. de Bruijn graphs, 8. empty graphs , 9. Hanoi graphs,

  3. 19/05/2000 · Claw-free graphs were originally investigated as natural generalizations to line graphs [58] and have since developed into the subject of a rich area of study in graph theory [59]. Line graphs are...

  4. 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 corresponding edges share an endpoint in G. A line graph L ( G ) cannot contain a claw, because if three edges e 1 , e 2 , and e 3 in G all share endpoints with another edge e 4 then by the pigeonhole principle at least two of e 1 , e 2 , and e 3 must share one ...

  5. 22/02/2022 · Graph Isomorphism for Graph Classes Characterized by Two Forbidden Induced Subgraphs Proceedings of WG 2012, Lecture Notes in Computer Science 7551, 34-45 (2012) GI-complete on line