Abstract
AbstractWe prove the following: Let G and $$G'$$
G
′
be two graphs on the same set V of v vertices, and let k be an integer, $$4\le k\le v-4$$
4
≤
k
≤
v
-
4
. If for all k-element subsets K of V, the induced subgraphs $$G_{\restriction K}$$
G
↾
K
and $$G'_{\restriction K}$$
G
↾
K
′
have the same numbers of 3-homogeneous subsets, the same numbers of $$P_4$$
P
4
’s, and the same numbers of claws or co-claws, then $$G'$$
G
′
is equal to G or to the complement $$\overline{G}$$
G
¯
of G. We give also a similar result whenever the same numbers are modulo a prime.
Publisher
Springer Science and Business Media LLC
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