“…. Thus we can see that the four vertex pairs (1,5), (1,6), (1,7) and (1,8) in CG r 8 have maximal distance 3 i.e., the four vertex pairs (8,4), (8,3), (8,2) and (8, 1) in CG 8 have the maximal distance 3.…”
Section: Upper Bound Of Conjecturementioning
confidence: 90%
“…It follows from ( 1) and (2) that the generating function for A-sequence of (C, zC) is 1 1−z . By Lemma 2.3, we obtain…”
Recently, in the paper [4] we suggested the two conjectures about the diameter of io-decomposable Riordan graphs of the Bell type. In this paper, we give a counterexample for the first conjecture. Then we prove that the first conjecture is true for the graphs of some particular size and propose a new conjecture. Finally, we show that the second conjecture is true for some special io-decomposable Riordan graphs.
“…. Thus we can see that the four vertex pairs (1,5), (1,6), (1,7) and (1,8) in CG r 8 have maximal distance 3 i.e., the four vertex pairs (8,4), (8,3), (8,2) and (8, 1) in CG 8 have the maximal distance 3.…”
Section: Upper Bound Of Conjecturementioning
confidence: 90%
“…It follows from ( 1) and (2) that the generating function for A-sequence of (C, zC) is 1 1−z . By Lemma 2.3, we obtain…”
Recently, in the paper [4] we suggested the two conjectures about the diameter of io-decomposable Riordan graphs of the Bell type. In this paper, we give a counterexample for the first conjecture. Then we prove that the first conjecture is true for the graphs of some particular size and propose a new conjecture. Finally, we show that the second conjecture is true for some special io-decomposable Riordan graphs.
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