Completely Independent Spanning Trees on 4-Regular Chordal Rings

Constructing Two Completely Independent Spanning Trees in Balanced Hypercubes

“…By Corollary 5,T 1 andT 2 are two CISTs of BH 3 and diam(T 1 ) = diam(T 2 ) = 16. Moreover, we observe that (1,1,2) is the unique center vertex ofT 1 and it is adjacent to a particular vertex (2,1,2). Also, (2, 0, 2) is the unique center vertex ofT 2 and it is adjacent to a particular vertex (3, 0, 2) (see Fig.…”

“…For constructing two CISTs, the results in [5], [13], [14], [23] are based on Theorem 1, and the results in [2], [21] are based on Theorem 2. In this paper, we apply Theorem 1 to construct two CISTs of balanced hypercubes.…”

“…Accordingly, researches investigating sufficient conditions for graphs that admit multiple CISTs, such as degree-based conditions, can be found in [1], [3], [7], [15], [17]. Also, with the help of constructions, it has been confirmed that certain classes of graphs possess two CISTs, e.g., 4-connected maximal planar graphs [13], Cartesian product of any 2-connected graphs [14], 4-regular chordal rings [2], [23], crossed cubes [5], and several hypercube-variant networks [21]. In addition, more graphs possessing multiple CISTs can be found in [6], [12], [16], [19], [20], [22].…”