the set of all non-increasing non-negative integer sequences $pi=(d_1‎, ‎d_2,ldots,d_n)$ is denoted by $ns_n$‎. ‎a sequence $piin ns_{n}$ is said to be graphic if it is the degree sequence of a simple graph $g$ on $n$ vertices‎, ‎and such a graph $g$ is called a realization of $pi$‎. ‎the set of all graphic sequences in $ns_{n}$ is denoted by $gs_{n}$‎. ‎the complete product split graph on $l‎ ...

An undirected graph G = (V, E) is a probe split graph if its vertex set can be partitioned into two sets, N (nonprobes) and P (probes) where N is independent and there exists E′ ⊆ N ×N such that G′ = (V, E ∪ E′) is a split graph. Recently Chang et al. gave an O(V (V +E)) time recognition algorithm for probe split graphs. In this article we give O(V 2 +V E) time recognition algorithms and charac...

Action recognition has been recognized as an activity in which individuals’ behaviour can be observed. Assembling profiles of regular activities such daily living support identifying trends the data during critical events. A skeleton representation human body proven to effective for this task. The skeletons are presented graphs form-like. However, topology a graph is not structured like Euclide...

Given a connected graph G and a terminal set R ⊆ V (G), Steiner tree asks for a tree that includes all of R with at most r edges for some integer r ≥ 0. It is known from [ND12,Garey et. al [1]] that Steiner tree is NP-complete in general graphs. Split graph is a graph which can be partitioned into a clique and an independent set. K. White et. al [2] has established that Steiner tree in split gr...

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 ...

In the SPLIT VERTEX DELETION problem, given a graph G and an integer k, we ask whether one can delete k vertices from the graph G to obtain a split graph (i.e., a graph, whose vertex set can be partitioned into two sets: one inducing a clique and the second one inducing an independent set). In this paper we study fixed-parameter algorithms for SPLIT VERTEX DELETION parameterized by k: we show t...

We show that the class of perfect graphs known as split graphs can be efficiently recognized in a parallel process environment. Given an undirected graph G = (V, E) with n vertices we define a subgraph G, = (AV, AE) and we prove some properties on G, leading to a constant-time parallel split graph recognition algorithm.