A graph G admits an H-covering if every edge of belongs to a subgraph isomorphic given H. is said be H-magic there exists bijection f:V(G)∪E(G)→{1,2,…,|V(G)|+|E(G)|} such that wf(H′)=∑v∈V(H′)f(v)+∑e∈E(H′)f(e) constant, for H′ In particular, H-supermagic f(V(G))={1,2,…,|V(G)|}. When H complete K2, H-(super)magic labeling edge-(super)magic labeling. Suppose F-covering and two graphs F We define (...

A (p, q)-graph G is called super edge-magic if there exists a bijective function f : V (G) ∪ E(G) → {1, 2, . . . , p + q} such that f(u)+f(v)+f(uv) is a constant for each uv ∈ E(G) and f(V (G)) = {1, 2, . . . , p}. In this paper, we introduce the concept of strong super edgemagic labeling as a particular class of super edge-magic labelings ∗Supported by Slovak VEGA Grant 1/4005/07. †Supported i...

The super connectivity κ ′ and the super edge-connectivity λ′ are more refined network reliability indices than connectivity κ and edge-connectivity λ. This paper shows that for a connected graph G with order at least four rather than a star and its line graph L(G), κ ′(L(G))= λ′(G) if and only if G is not super-λ′. As a consequence, we obtain the result of Hellwig et al. [Note on the connectiv...

Let G = (V, E) be a connected graph. Let G = (V, E) be a connected graph. An edge set F ⊂ E is said to be a k-restricted edge cut, if G− F is disconnected and every component of G− F has at least k vertices. The k-restricted edge connectivity of G, denoted by λk(G), is the cardinality of a minimum k-restricted edge cut of G. A graph G is λk-connected, if G contains a k-restricted edge cut. A λk...

The super line graph of index r of a graph G has the r-sets of edges as its vertices, with two being adjacent if one has an edge that is adjacent to an edge in the other. In this paper, we continue our investigation of this graph by establishing two results, the first on the independence number of super line graphs of arbitrary index and the second on pancyclicity in the index-2 case.

Let G = (V,E) be a multigraph (it has multiple edges, but no loops). We call G maximally edge-connected if λ(G) = δ(G), and G super edge-connected if every minimum edge-cut is a set of edges incident with some vertex. The restricted edgeconnectivity λ′(G) of G is the minimum number of edges whose removal disconnects G into non-trivial components. If λ′(G) achieves the upper bound of restricted ...