For a multi-set E of splits {bipartitions) of a finite set X, we introduce the multi-split graph G(E). This graph Is a natural extension of the Buneman graph. Indeed, it is shown that several results pertaining to the Buneman graph extend to the multi-split graph. In addition, in case E is derived from a set R of partitions of X by taking parts together with their complements, we show that the ...

A graph is called supermagic if there is a labeling of edges where the edges are labeled with consecutive distinct positive integers such that the sum of the labels of all edges incident with any vertex is constant. A graph G is called degree-magic if there is a labeling of the edges by integers 1, 2, ..., |E(G)| such that the sum of the labels of the edges incident with any vertex v is equal t...

‎we investigate two constructions‎ - ‎the replacement and the zig-zag‎ ‎product of graphs‎ - ‎describing several fascinating connections‎ ‎with combinatorics‎, ‎via the notion of expander graph‎, ‎group‎ ‎theory‎, ‎via the notion of semidirect product and cayley graph‎, ‎and‎ ‎with markov chains‎, ‎via the lamplighter random walk‎. ‎many examples‎ ‎are provided‎.

A problem is said to be GI-complete if it is provably as hard as graph isomorphism; that is, there is a polynomial-time Turing reduction from the graph isomorphism problem. It is known that the GI problem is GI-complete for some special graph classes including regular graphs, bipartite graphs, chordal graphs and split graphs. In this paper, we prove that deciding isomorphism of double split gra...

A graph G is called a split graph if the vertex-set V of G can be partitioned into two subsets V1 and V2 such that the subgraphs of G induced by V1 and V2 are empty and complete, respectively. In this paper, we characterize hamiltonian graphs in the class of split graphs with minimum degree δ at least |V1| − 2.

In this paper, the exact formulae for the generalized degree distance, degree distance and reciprocal degree distance of strong product of a connected and the complete multipartite graph with partite sets of sizes m0, m1, . . . , mr&minus1 are obtained. Using the results obtained here, the formulae for the degree distance and reciprocal degree distance of the closed and open fence graphs are co...

in this paper, we introduce the notions of product vague graph, balanced product vague graph, irregularity and total irregularity of any irregular vague graphs and some results are presented. also, density and balanced irregular vague graphs are discussed and some of their properties are established. finally we give an application of vague digraphs.

The concept of connectedness plays an important role in many networks. Digraphs are considered as an excellent modeling tool and are used to model many types of relations amongst any physical situations. In this paper the concept of strong non-split domination in directed graph D has been introduced by considering the dominating set S is a strong non-split dominating set if the complement of S ...