Symmetric graph designs, or SGDs, were deened by Gronau et al. as a common generalisation of symmetric BIBDs and orthogonal double covers. This note gives a classiication of SGDs admitting a 2-transitive automorphism group. There are too many for a complete determination, but in some special cases the determination can be completed, such as those which admit a 3-transitive group, and those with...

Let s be a positive integer. A graph is s-transitive if its automorphism group is transitive on s-arcs but not on (s + 1)-arcs. Let p be a prime. In this article a complete classification of tetravalent s-transitive graphs of order 3p is given.

Let s be a positive integer. A graph is s-transitive if its automorphism group is transitive on s-arcs but not on (s + 1)-arcs. Let p be a prime. In this article a complete classification of tetravalent s-transitive graphs of order 3p is given.

Let Γ be a graph and let G be a group of automorphisms of Γ. The graph Γ is called G-normal if G is normal in the automorphism group of Γ. Let T be a finite non-abelian simple group and let G = T l with l ≥ 1. In this paper we prove that if every connected pentavalent symmetric T -vertex-transitive graph is T -normal, then every connected pentavalent symmetric G-vertex-transitive graph is G-nor...

The chromatic symmetric function of a graph is a symmetric function that generalizes the chromatic polynomial. Its investigation has largely been motivated by the existence of an open problem, the poset-chain conjecture, which is equivalent to the assertion that for certain graphs, the coefficients in the expansion of the chromatic symmetric function in terms of elementary symmetric functions, ...

A tricirculant is a graph admitting a non-identity automorphism having three cycles of equal length in its cycle decomposition. A graph is said to be symmetric if its automorphism group acts transitively on the set of its arcs. In this paper it is shown that the complete bipartite graph K3,3, the Pappus graph, Tutte’s 8-cage and the unique cubic symmetric graph of order 54 are the only connecte...

‎the harmonic index of a connected graph $g$‎, ‎denoted by $h(g)$‎, ‎is‎ ‎defined as $h(g)=sum_{uvin e(g)}frac{2}{d_u+d_v}$‎ ‎where $d_v$ is the degree of a vertex $v$ in g‎. ‎in this paper‎, ‎expressions for the harary indices of the‎ ‎join‎, ‎corona product‎, ‎cartesian product‎, ‎composition and symmetric difference of graphs are‎ ‎derived‎.