Topological and Communication Aspects of Hyper-Star Graphs

Computing the Wide Diameter of Regular Hyper-Star Networks Using Independent Spanning Trees

“…length either 3 or 4). This determines the fault and wide diameters of HS (4,2). For k≥3, the fault and wide diameters of HS(2k,k) can be obtained by Lemmas 1 and 4.…”

“…Hence, subsequent researches particularly focused on the regular hyper-stars for intensifying their properties [4][5][6][7][8]. Figure 1 shows the graph HS (6,3), where each vertex is labeled by its binary representation and octal representation.…”

“…One of the central issues on the properties of interconnection networks is to consider the symmetry. Fortunately, HS(2k,k) has been proved to be vertex-symmetric in [4]. Lee et al [5] showed that HS(2k,k) has diameter 2k-1 and connectivity k, and thus is maximally fault-tolerant (i.e., the connectivity is equal to its regularity).…”

“…Although the fault diameter of HS(2k,k) has already known in [4] (see Lemma 1), the current research result with regard to the wide diameters of HS(2k,k) is not clear except that a bound appeared in [4]. Our technique is the use of analyzing the heights of a set of particular spanning trees, called independent spanning trees (introduced in Section 3), to drawing a definite conclusion of the wide diameter.…”

Embedding Algorithms of Hierarchical Folded HyperStar Network

“…이러한 하이퍼큐브 연결망을 기반으로 하면 서 변형된 연결망 구조로 [1,7,12]이 있으며, 하이퍼큐브를 기반으로 계층적 상호연결망 형태를 갖는 HCN(n,n) [14], HFN(n,n) [3] 등이 분석되었다 [8,9,15]. 폴디드 하이퍼스타 연결망은 그 래프이론 관점에서 좋은 성질을 갖는 하이퍼스타 연결망의 지름(diameter)을 1/2 정도 개선하기 위해 제안된 연결망이 다 [9,16].…”