Counting pure k cycles in sequences of Cayley graphs

Enumeration of disjoint Hamilton cycles in a divisor Cayley graph

“…The following corollary is immediate from the Theorem 3.3. Step 1: For the divisor d = 5, the 5 disjoint cycles of length 3 are (0, 5, 10, 0), (1,6,11,1) , (2,7,12,2) , (3,8,13,3) and (4,9,14,4).…”

“…The cycle structure of Cayley graphs and Unitary Cayley graphs were studied by Berrizbeitia and Guidici [1,2] and Detzer and Guidici [6]. Recently Maheswari and Madhavi [8][9][10] studied the enumeration methods for finding the number of triangles and Hamilton cycles in arithmetic graphs associated with the quadratic residues modulo a prime p and the Euler totient function ϕ(n) , n ≥ 1 an integer.…”

Enumeration of Triangles in Cayley Graphs

“…The cycle structure of Cayley graphs associated with certain arithmetic functions were studied by Berrizbeitia and Giudici [2][3] and Dejter and Giudici [5]. Maheswari and Madhavi [7] [8] enumerated Hamilton cycles and triangles in arithmetic Cayley graphs associated with Euler totient function and quadratic residues modulo a prime.…”

“…In [2] Berrizbeitia and Giudici consider sequences of Cayley graphs ( , ) n n Cay G S satisfying the multiplicative arithmetic property, where n G is a finite abelian group and n S is a subset of where n Z is the ring of integers modulo n and n U is the multiplicative group of units modulo n . In this paper we give a formula for determining the number of triangles in a Cayley graph ( , ) G X S where X is a finite group, not necessarily abelian and S is a symmetric subset of X .…”

Graphs of Permutation Groups

“…Dejter and Giudici [1], Berrizabeitia and Giudici [2] and others have studied the cycle structure of graphs associated with certain number theoretic functions. Maheswari and Madhavi [3,4] studied the Hamilton cycles and triangles of the algebraic graphs associated with Euler totient function () n  1, n  an integer and quadratic residues modulo a prime .…”