Minimum average congestion of enhanced and augmented hypercubes into complete binary trees

A Tight Bound for Congestion of an Embedding

“…The dilation problem, congestion problem and the wirelength problem are different in the sense that an embedding that gives the minimum dilation need not give the minimum congestion or the minimum wirelength and vice-versa. Even though there are numerous results and discussions on the congestion problem, there is no efficient method to compute exact congestion of graph embeddings [4,5,15]. In recent years, Manuel et al obtained a lower bound for dilation of an embedding using minimum wirelength and formulated the result as IPS Lemma [25], and in 2014 the same authors computed an improved bound without using wirelength and formulated the result as Dilation Lemma [26].…”

“…Therefore, a minimum congestion is a most desirable feature in network embedding [3]. Congestion of an embedding has been well studied for a number of networks [4][5][6][7][8].…”

Embedding of Recursive Circulants into Certain Necklace Graphs

“…Graph embeddings have been well studied for hypercubes into cycles [9,10], star graph into path [11], generalized wheels into arbitrary trees [12], enhanced and augmented hypercubes into complete binary trees [13], circulant into arbitrary trees, cycles, certain multicyclic graphs and ladders [14], hypercubes into cylinders, snakes and caterpillars [15], 1-fault hamiltonian graphs into wheels and fans [16], hypercubes into necklace, windmill and snake graphs [17], circulant into necklace and windmill graphs [18], recursive circulants into certain trees [19].…”

Conditional Diagnosability of Complete Josephus Cubes

“…Definition 2. [13,10] The enhanced hypercube, denoted by EQ n,k , is a graph with the vertex set V (EQ n,k ) = {a n a n−1 · · · a 1 | a i ∈ {0, 1}, i ∈ {1, 2, . .…”