Due to the increasing amount of video data, a lot of research has been done in the field of retrieving and categorizing this type of data. On the other hand, with the growing popularity of football and the increasing number of its audiences, the importance of automatic and real-time extraction of statistics and information about soccer matches has increased. One of the critical and challenging tasks in soccer video analysis is the detection of players’ blobs and regions, along with identifying the teams related to the players. This task encounters many challenges, including grass loss in the playfield, the presence of playfield lines and players' shadows, the overlapping of players with objects and other players, and different shapes of players in different situations. This paper proposes a framework for detecting players and their related teams. For this purpose, an object-sieve-based method is used to detect players’ blobs, and a genetic algorithm is used to identify their related teams. Each chromosome of the genetic algorithm is a window that lies on one blob whose fitness function shows how much its color and shape characteristics fit with the uniforms of each of the two teams. The proposed method was evaluated by 50 different frames of broadcast soccer videos, including 563 players, and 40 different sub-images, including 84 players. The results show 98% and 91.6% precision for player detection and labeling, respectively.

Data mining is a powerful new technology to extract hidden information from data warehouses. Data mining analyzes data from different perspectives and  finds useful patterns and knowledge from large volumes of raw data. Clustering is one of the main methods of data mining. K-means algorithm is one of the most common clustering algorithms due to its efficiency and ease of use. One of the challenges of clustering is to identify the appropriate label for each cluster. The selection of a label is done so as to provide a proper description of cluster records. In some cases, choosing an appropriate label is not easy due to the results and structure of each cluster. The aim of this study is to present an algorithm based on the K-means clustering in order to facilitate the allocation of labels to each cluster.

A difference labeling of a graph G is an injective function f: V (G) → N ∪ {0} together with the weight function f∗ on E(G) given by f∗(uv) = |f(u)-f(v)| for every edge uv in G. The collection of subgraphs induced by the edges of the same weight is a decomposition of G and is called the common weight decomposition of G induced by f. Let ϒf denote the collection of all the paths taken from each member of the common weight decomposition induced by f. A difference labeling f of G is said to be a graphoidal difference labeling if ϒf is an acyclic graphoidal decomposition of G. This paper initiates a study on this concepts.

Let G be a graph and f: V (G)! {1, 2, 3, . . . . . |V (G)|} be a bijection. Let puv = f(u)f(v) and duv =        hf(u) f(v) i if f(u)  f(v) hf(v) f(u)i if f(v)  f(u) for all edge uv 2 E(G). For each edge uv assign the label 1 if gcd(puv, duv) = 1 or 0 otherwise. f is called PD-prime cordial labeling if |ef (0) − ef (1)|  1 where ef (0) and ef (1) respectively denote the number of edges labelled with 0 and 1. A graph with admit a PD-prime cordial labeling is called PD-prime cordial graph.

Let G be a graph with vertex set V (G) and edge set E(G), a vertex labeling f: V (G)! Z2 induces an edge labeling f+: E(G)! Z2 defined by f+(xy) = f(x) + f(y), for each edge xy 2 E(G). For each i 2 Z2, let vf (i) = |{u 2 V (G): f(u) = i}| and ef+(i) = |{xy 2 E(G): f+(xy) = i}|. A vertex labeling f of a graph G is said to be friendly if |vf (1) − vf (0)|  1. The friendly index set of the graph G, denoted by FI(G), is defined as {|ef+(1) − ef+(0)|: the vertex labeling f is friendly}. The full friendly index set of the graph G, denoted by FFI(G), is defined as {ef+(1) − ef+(0): the vertex labeling f is friendly}. A graph G is cordial if − 1, 0 or 1 2 FFI(G). In this paper, by introducing labeling subgraph embeddings method, we determine the cordiality of a family of cubic graphs which are double-edge blow-up of P2 × Pn, n  2. Consequently, we completely determined friendly index and full product cordial index sets of this family of graphs.