We study a class of Cayley graphs as models for interconnection networks. With focus on efficient communication we prove that for any graph in the class there exists a gossiping protocol which exhibits attractive features, and moreover we give an algorithm for constructing such a protocol. In particular, these hold for two important subclasses of graphs, namely, Cayley graphs admitting a comple...

A regular covering projection ℘: X̃ → X of connected graphs is G-admissible if G lifts along ℘. Denote by G̃ the lifted group, and let CT(℘) be the group of covering transformations. The projection is called G-split whenever the extension CT(℘) → G̃ → G splits. In this paper, split 2-covers are considered, with a particular emphasis given to cubic symmetric graphs. Supposing that G is transitive o...

a graph is textit{symmetric}, if its automorphism group is transitive on the set of its arcs. in this paper, we  classifyall the connected cubic symmetric  graphs of order $36p$  and $36p^{2}$, for each prime $p$, of which the proof depends on the classification of finite simple groups.

We present a new construction of infinite families of (finite as well as infinite) vertex-transitive graphs that are not Cayley graphs; many of these turn out even to be arc-transitive. The construction based on representing vertex-transitive graphs as coset graphs of groups, and on a simple but powerful necessary arithmetic condition for Cayley graphs. Vertex-transitive graphs are interesting ...

recently, hua et al. defined a new topological index based on degrees and inverse ofdistances between all pairs of vertices. they named this new graph invariant as reciprocaldegree distance as 1{ , } ( ) ( ( ) ( ))[ ( , )]rdd(g) = u v v g d u  d v d u v , where the d(u,v) denotesthe distance between vertices u and v. in this paper, we compute this topological index forgrassmann graphs.

A (directed) cycle C in a graph is called consistent provided there exists an automorphism of , acting as a 1-step rotation of C. A beautiful but not well-known result of J.H. Conway states that if is arc-transitive and has valence d, then there are precisely d − 1 orbits of consistent cycles under the action of Aut( ). Contract grant sponsor: Javna agencija za raziskovalno dejavnost Republike ...

we find recursive formulae for the number of perfect matchings in a graph g by splitting g into subgraphs h and q. we use these formulas to count perfect matching of p hypercube qn. we also apply our formulas to prove that the number of perfect matching in an edge-transitive graph is , where denotes the number of perfect matchings in g, is the graph constructed from by deleting edges with an en...

I describe a 27-vertex graph that is vertex-transitive and edgetransitive but not 1-transitive. Thus while all vertices and edges of this graph are similar, there are no edge-reversing automorphisms. A graph (undirected, without loops or multiple edges) is said to be vertextransitive if its automorphism group acts transitively on the set of vertices, edge-transitive if its automorphism group ac...

The graphs in this paper are finite, undirected, and without loops, but may have more than one edge between a pair of vertices. If such graph has ℓ edges, then an Euler cycle is sequence (e1,e2,…,eℓ) these each occurring exactly once, that ei, ei + 1 incident with common vertex for i (reading subscripts modulo ℓ). An symmetrical if there exists automorphism the → 2 i. cyclic group generated by ...