The L(p, q)-Edge-Labelling problem is the edge variant of well-known q)-Labelling problem. It equivalent to itself if we restrict input latter line graphs. So far, complexity was only partially classified in literature. We complete this study for all $$p,q\ge 0$$ by showing that whenever $$(p,q)\ne (0,0)$$ , NP-complete. do proving except $$p=q=0$$ there an integer k so L (p q)-Edge-k -Labelling

A total labelling of a graph over an abelian group is a bijection from the set of vertices and edges onto the set of group elements. A labelling can be used to define a weight for each edge and for each vertex of finite degree. A labelling is edge-magic if all the edges have the same weight and vertex-magic if all the vertices are finite degree and have the same weight. We exhibit magic labelli...

The problem of Radio Labelling is to assign distinct integer labels to all the vertices of a graph, such that adjacent vertices get labels at distance at least two. The objective is to minimize the label span. Radio labelling is a combinatorial model for frequency assignment in case that the transmitters are not allowed to operate at the same channel. We show that radio labelling is related to ...

We examine decompositions of complete graphs with an even number of vertices, K2n, into n isomorphic spanning trees. While methods of such decompositions into symmetric trees have been known, we develop here a more general method based on a new type of vertex labelling, called flexible q-labelling. This labelling is a generalization of labellings introduced by Rosa and Eldergill.

Applying the recently obtained distributive lattice structure on the set of 1-factors, we show that the resonance graphs of any benzenoid systems G, as well as of general plane (weakly) elementary bipartite graphs, are median graphs and thus extend greatly Klavžar et al.’s result. The n-dimensional vectors of nonnegative integers as a labelling for the 1-factors of G with n inner faces are desc...

The (d,1)-total labelling of graphs was introduced by Havet and Yu. In this paper, we consider the list version of (d,1)-total labelling of graphs. Let G be a graph embedded in a surface with Euler characteristic ε whose maximum degree ∆(G) is sufficiently large. We prove that the (d,1)-total choosability C d,1(G) of G is at most ∆(G) + 2d.

‎in this paper we introduce mixed unitary cayley graph $m_{n}$‎ ‎$(n>1)$ and compute its eigenvalues‎. ‎we also compute the energy of‎ ‎$m_{n}$ for some $n$‎.