the edge tenacity te(g) of a graph g is dened as:te(g) = min {[|x|+τ(g-x)]/[ω(g-x)-1]|x ⊆ e(g) and ω(g-x) > 1} where the minimum is taken over every edge-cutset x that separates g into ω(g - x) components, and by τ(g - x) we denote the order of a largest component of g. the objective of this paper is to determine this quantity for split graphs. let g = (z; i; e) be a noncomplete connected spli...

Families of edge transitive algebraic graphs defined over finite commutative rings were used for the development of stream ciphers, public key cryptosystems and key exchange protocols. We present the results of the first implementation of a public key algorithm based on the family of algebraic graphs, which are not edge transitive. The absence of an edge transitive group of symmetries means tha...

A list is given of all semisymmetric (edgebut not vertex-transitive) connected finite cubic graphs of order up to 768. This list was determined by the authors using Goldschmidt’s classification of finite primitive amalgams of index (3, 3), and a computer algorithm for finding all normal subgroups of up to a given index in a finitely-presented group. The list includes several previously undiscov...

We explore properties of edge colorings of graphs defined by set intersections. An edge coloring of a graphG with vertex set V ={1,2, . . . ,n} is called transitive if one can associate sets F1,F2, . . . ,Fn to vertices of G so that for any two edges ij,kl∈E(G), the color of ij and kl is the same if and only if Fi∩Fj =Fk∩Fl. The term transitive refers to a natural partial order on the color set...