Domination numbers on the complement of the Boolean function graph of a graph

Abstract

Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This document has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library http://dml.cz 130 (2005) MATHEMATICA BOHEMICA No. 3, 247-263 DOMINATION NUMBERS ON THE COMPLEMENT OF THE BOOLEAN FUNCTION GRAPH OF A GRAPH

$P_4$-Decomposition in Boolean function graph of $B_3(G)$

“…∼ = (n(n−2)/2)P 4 and N (4) ∼ = (n/2)P 4 , N (5) ∼ = (n(n− 2))P 4 , N (6) ∼ = nP 4 . Hence, B 3 (C + n )−nK 2 is P 4 -decomposable.…”

“…The edge set of 2n 2 − 3n P 4 is given by the edge sets N (5) , N (6) as in Case 1 and the sets N (7) and N (8) , where…”

“…The edge set of 2nK 2 is given by the set U n i=1 {(v, f i ) , (u i , e i )} . The edge set of 11n 2 − 5n /6 P 4 is given by the edge sets Q (2) , Q (3) , Q (4) , Q (5) as in Theorem 3.6 and the set Q (9) where, Q (9) =U (n−1)/3 j=1 U n i=1 Q (9) ji , Q…”

“…Then the edge set of B 3 K + 1,n can be decomposed into 11n 2 − 7n /6 P 4 and 3nK 2 . The edge set of 3nK 2 is given by the set U n i=1 (v, f i ) , (u i , e i ) , v i , e i+(2n−3)/3 The edge set of 11n 2 − 7n /6 P 4 is given by the edge sets Q (4) , Q (5) , Q (8) as in Theorem 3.6 and the set Q (10) , where Q (10) =U…”