The(a,d)-H-total Labeling Of Some Graphs

Since Rosa introduced the concept about graceful labeling of graphs in the 1960s, many scholars have studied the graceful labeling of graphs deeply. With the development of science and technology, many scholars also defined some new concepts of graph labeling. So far, scholars have published more than a thousand articles on graph labeling. Graph labeling is widely applied in the following fields, such as coding theory, radar, circuit design, and communication network.Labeling of magic type is derived from magic square. Super (a, d)-H-total labeling is one of labeling with strict conditions, and it has extensive connections with other types of labelings. (a, d)-H-total labeling is closely related to graph labeling, graph decomposition, graph covering and magic square and it arouses more and more people’s concerns. The main contents of this study are as follows:(1). Using algebraic method and d-column matrix, we study the super (a, d)-H-total labeling problem of PCG(H,G,n), when d=0,1,2,3,4.(2). For some d, we have resolved the problem about super (b,d)-H-total labeling of mG with construction method, and obtained the following result:if G is a super (a, d)-H-total graph, then mG is a super (b, d)-H-total graph.(3). We have completely solved the problem about (a,0)-C3-total labeling of wheel graph Wn and find a super (a,1)-C3-total labeling of wheel graph Wn(4). Super (a, d)-edge-labeling problem of friendship graph Fn is solved.(5). Some d-column matrices are constructed.