in this paper, we prove the existence of fixed point for chatterjea type mappings under $c$-distance in cone metric spaces endowed with a graph. the main results extend, generalized and unified some fixed point theorems on $c$-distance in metric and cone metric spaces.

The Gallai graph and the anti-Gallai graph of a graph G are edge disjoint spanning subgraphs of the line graph L(G). The vertices in the Gallai graph are adjacent if two of the end vertices of the corresponding edges in G coincide and the other two end vertices are nonadjacent in G. The anti-Gallai graph of G is the complement of its Gallai graph in L(G). Attributed to Gallai (1967), the study ...

The inflation $G_{I}$ of a graph $G$ with $n(G)$ vertices and $m(G)$ edges is obtained from $G$ by replacing every vertex of degree $d$ of $G$ by a clique, which is isomorph to the complete graph $K_{d}$, and each edge $(x_{i},x_{j})$ of $G$ is replaced by an edge $(u,v)$ in such a way that $uin X_{i}$, $vin X_{j}$, and two different edges of $G$ are replaced by non-adjacent edges of $G_{I}$. T...

In this paper we introduce a mixed approach for the semi-supervised data problem. Our approach consists of an ensemble unsupervised learning part where the labeled and unlabeled points are segmented into clusters. Continuing, we take advantage of the a priori information of the labeled points to assign classes to clusters and proceed to predicting with the ensemble method new incoming ones. Thu...

Object tracking is widely used in many applications such as intelligent surveillance, scene understanding, and behavior analysis. Graph-based semisupervised learning has been introduced to deal with specific tracking problems. However, existing algorithms following this idea solely focus on the pairwise relationship between samples and hence could decrease the classification accuracy for unlabe...

Conventional graph-based semi-supervised learning methods predominantly focus on single label problem. However, it is more popular in real-world applications that an example is associated with multiple labels simultaneously. In this paper, we propose a novel graph-based learning framework in the setting of semi-supervised learning with multiple labels. This framework is characterized by simulta...

Constructing an informative and discriminative graph plays an important role in the graph based semi-supervised learning methods. Among these graph construction methods, low-rank representation based graph, which calculates the edge weights of both labeled and unlabeled samples as the low-rank representation (LRR) coefficients, has shown excellent performance in semi-supervised learning. In thi...

Given a group or semi-group Γ generated (in the sense of semi-groups) by some subset S ⊂ Γ, the Cayley graph of Γ with respect to S is the oriented graph having vertices γ ∈ Γ and oriented edges (γ, γs)s∈S . In this paper, we consider generating sets S which are not necessarily finite thus yielding oriented Cayley graphs which are perhaps not locally finite. The above situation gives rise to a ...

A graph G is said to be hyper-connected if the removal of every minimum cut creates exactly two connected components, one of which is an isolated vertex. In this paper, we first generalize the concept of hyper-connected graphs to that of semi-hyper-connected graphs: a graph G is called semi-hyper-connected if the removal of every minimum cut of G creates exactly two components. Then we characte...