Identifying codes of the direct product of two cliques

Identifying Codes of Cartesian Product of Two Cliques of the Same Size

We determine the minimum cardinality of an identifying code of Kn Kn, the Cartesian product of two cliques of same size. Moreover we show that this code is unique, up to row and column permutations, when n ≥ 5 is odd. If n ≥ 4 is even, we exhibit two distinct optimal identifying codes.

Identifying Codes and Domination in the Product of Graphs

An identifying code in a graph is a dominating set that also has the property that the closed neighborhood of each vertex in the graph has a distinct intersection with the set. The minimum cardinality of an identifying code in a graph G is denoted γ(G). We consider identifying codes of the direct product Kn × Km. In particular, we answer a question of Klavžar and show the exact value of γ(Kn×Km...

On the Grobner Basis of a Family of Quasi-Cyclic LDPC Codes

ID Codes in Cartesian Products of Cliques

An identifying code in a graph G is a set D of vertices such that the closed neighborhood of each vertex of the graph has a nonempty, distinct intersection with D. The minimum cardinality of an identifying code is denoted γ(G). Building upon recent results of Gravier, Moncel, and Semri, we show for n ≤ m that γID(Kn Km) = max{2m−n,m+⌊n/2⌋}. Furthermore, we improve upon the bounds for γ(G Km) an...

مطالعه تطبیقی لوگوتایپ‌های مصور مطبوعاتی و نشانه‌های فرهنگی در شعر دوره مشروطه

Iranian graphic designers made their first efforts to create modern logotypes, called Sar- Onvan (Subtitle), in Qajar era. These works, which are considered as important parts of the background of Iranian graphic design, worth adequate attention; through studying them, we may discover their special visual expressions leading us to a better understanding of the specific social situation in Qajar...