For a graph Γ with vertex set V , a subset C of V is called a perfect code [16] of Γ if every vertex of Γ is at distance no more than one to exactly one vertex in C. In other words, C is a perfect code in Γ provided that C is independent in Γ and every vertex of V \ C is adjacent to precisely one vertex of C.
Aug 19, 2020
Oct 7, 2022 · In this paper, we give some necessary conditions of a subgroup of a given group being a (total) perfect code in a Cayley sum graph of the group.
Oct 7, 2022 · In this paper, we give some necessary conditions of a subgroup of a given group being a (total) perfect code in a Cayley sum graph of the group.
Apr 18, 2020 · A subset C of G is called a perfect code of G if there exists a Cayley sum graph of G which admits C as a perfect code. In particular, if a ...
In Section 3, we focus on the study of subgroup perfect codes in Cayley sum graphs. After showing an easy necessary and sufficient condition, we mainly prove a ...
In Section 3, we focus on the study of subgroup perfect codes in Cayley sum graphs. After showing an easy necessary and sufficient condition, we mainly prove a ...
Jan 28, 2022 · A subset C C of the vertex set of a graph Γ Γ is called a perfect code of Γ Γ if every vertex of Γ Γ is at distance no more than one to exactly ...
Apr 29, 2024 · Every non-trivial subgroup of G with even order is a subgroup total perfect code of G if and only if G is isomorphic to Z 2 n with n ≥ 2 , or Z ...
Jul 1, 2020 · A subset C of G is called a perfect code of G if there exists a Cayley sum graph of G which admits C as a perfect code. In particular, if a ...
7 days ago · In this paper, we give some necessary conditions of a subgroup of a given group being a (total) perfect code in a Cayley sum graph of the group.