NOTE ON SEED GRAPHS WITH COMPONENTS OF GIVEN ORDER
Acta mathematica Universitatis Comenianae, Tome 69 (2000) no. 1
D. Froncek. NOTE ON SEED GRAPHS WITH COMPONENTS OF GIVEN ORDER. Acta mathematica Universitatis Comenianae, Tome 69 (2000) no. 1. http://geodesic.mathdoc.fr/item/AMUC_2000_69_1_a6/
@article{AMUC_2000_69_1_a6,
     author = {D. Froncek},
     title = {NOTE {ON} {SEED} {GRAPHS} {WITH} {COMPONENTS} {OF} {GIVEN} {ORDER}},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {2000},
     volume = {69},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2000_69_1_a6/}
}
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Voir la notice de l'article provenant de la source Comenius University

A closed neighbourhood $N_G[x]$ of a vertex $x$ in a graph $G$ is the subgraph of $G$ induced by $x$ and all neighbours of $x$. A seed of a vertex $x\in G$ is the subgraph of $G$ induced by all vertices of $G\setminus N_G[x]$ and we denote it by $S_G(x)$. A graph $F$ is a seed graph if there exists a graph $G$ such that $S_G(x)\cong F$ for each $x\in G$. In this paper seed graphs with more than two components are studied. It is shown that if all components are of equal order, then they are all isomorphic to a complete graph. In the general case it is shown how the structure of any component $F_i$ of a seed graph $F$ depends on the structure of all components of smaller order.