A new transitive closur ealgorithm is presented for implication graphs that c ontainpartial implications. In the presence of partial implications, a vertex can assume the true state when all vertices that p artially imply it become true. Such graphs provide a more complete representation of a logic cir cuit than is possible with the conventional pair-wise implications. A napplic ation of the ne...

A graph G is k-ordered if for any sequence of k distinct vertices v1, v2, . . . , vk of G there exists a cycle in G containing these k vertices in the specified order. In 1997, Ng and Schultz posed the question of the existence of 3-regular 4-ordered graphs other than K4 and K3,3. In 2008, Meszaros solve the question by proving the Petersen graph and the Heawood graph are 3-regular 4-ordered gr...

In this paper we examine the orders of vertex-transitive self-complementary uniform hypergraphs. In particular, we prove that if there exists a vertex-transitive selfcomplementary k-uniform hypergraph of order n, where k = 2 or k = 2 + 1 and n ≡ 1 (mod 2), then the highest power of any prime dividing n must be congruent to 1 modulo 2. We show that this necessary condition is also sufficient in ...

A graph is vertex-transitive if its automorphism group acts transitively on its vertices. A vertex-transitive graph is a Cayley graph if its automorphism group contains a subgroup acting regularly on its vertices. In this paper, the cubic vertextransitive non-Cayley graphs of order 8p are classified for each prime p. It follows from this classification that there are two sporadic and two infini...

In the graph theory, two graphs are said to be isomorphic if there is a one-one, onto mapping defined between their set of vertices so as to preserving the adjacency between vertices. An isomorphism defined on a vertex set of a graph to itself is called automorphism of the given graph. Two vertices in a graph are said to be similar if there is an automorphism defined on its vertex set mapping o...

For random walks on finite graphs, we record some equalities, inequalities and limit theorems (as the size of graph tends to infinity) which hold for vertex-transitive graphs but not for general regular graphs. The main result is a sharp condition for asymptotic exponentiality of the hitting time to a single vertex. Another result is a lower bound for the coefficient of variation of hitting tim...

Hamidoune’s connectivity results [11] for hierarchical Cayley digraphs are extended to Cayley coset digraphs and thus to arbitrary vertex transitive digraphs. It is shown that if a Cayley coset digraph can be hierarchically decomposed in a certain way, then it is optimally vertex connected. The results are obtained by extending the methods used in [11]. They are used to show that cycle-prefix g...