a graph g is said to have a totally magic cordial labeling with constant c if there exists a mapping f : v (g) ∪ e(g) → {0, 1} such that f(a) + f(b) + f(ab) ≡ c (mod 2) for all ab ∈ e(g) and |nf (0) − nf (1)| ≤ 1, where nf (i) (i = 0, 1) is the sum of the number of vertices and edges with label i. in this paper, we give a necessary condition for an odd graph to be not totally magic cordial and ...

Knowledge representation of networked systems is fundamental in many disciplines. To date, existing methods for learning primarily focus on networks with simplex labels, yet real-world objects (nodes) are inherently complex nature and often contain rich semantics or labels. For example, a user may belong to diverse interest groups social network, resulting multi-label applications. A network no...

a vertex irregular total k-labeling of a graph g with vertex set v and edge set e is an assignment of positive integer labels {1, 2, ..., k} to both vertices and edges so that the weights calculated at vertices are distinct. the total vertex irregularity strength of g, denoted by tvs(g)is the minimum value of the largest label k over all such irregular assignment. in this paper, we study the to...

A large family of graph-based semi-supervised algorithms have been developed intuitively and pragmatically for the multi-label learning problem. These methods, however, only implicitly exploited the label correlation, as either part of graph weight or an additional constraint, to improve overall classification performance. Despite their seemingly quite different formulations, we show that all e...

The implicit graph conjecture states that every sufficiently small, hereditary graph class has a labeling scheme with a polynomial-time computable label decoder. We approach this conjecture by investigating classes of label decoders defined in terms of complexity classes such as P and EXP. For instance, GP denotes the class of graph classes that have a labeling scheme with a polynomial-time com...

The graph in this paper discussed are undirected、no multiple edges and simple graph, the unorganized state of definitions and terminology and the symbols in this graph referred to reference[2][3]. There are two kinds of labels of the graph: one is the reduced label, is to say that in order to get the label of one edge you should reduce the endpoints of the edge; the other is additive label, for...