In a graph G, the first and second degrees of a vertex v is equal to thenumber of their first and second neighbors and are denoted by d(v/G) andd 2 (v/G), respectively. The first, second and third leap Zagreb indices are thesum of squares of second degrees of vertices of G, the sum of products of second degrees of pairs of adjacent vertices in G and the sum of products of firs...

By d(v|G) and d_2(v|G) are denoted the number of first and second neighborsof the vertex v of the graph G. The first, second, and third leap Zagreb indicesof G are defined asLM_1(G) = sum_{v in V(G)} d_2(v|G)^2, LM_2(G) = sum_{uv in E(G)} d_2(u|G) d_2(v|G),and LM_3(G) = sum_{v in V(G)} d(v|G) d_2(v|G), respectively. In this paper, we generalizethe results of Naji et al. [Commun. Combin. Optim. ...

The first and second Zagreb indices of a graph are equal, respectively, to the sum of squares of the vertex degrees, and the sum of the products of the degrees of pairs of adjacent vertices. We now consider analogous graph invariants, based on the second degrees of vertices (number of their second neighbors), called leap Zagreb indices. A number of their basic properties is established.

To study the block structure of a connected graph G = (V,E), we introduce two algebraic approaches that reflect this structure: a binary operation + called a leap operation and a ternary relation L called a leap system, both on a finite, nonempty set V . These algebraic structures are easily studied by considering their underlying graphs, which turn out to be block graphs. Conversely, we define...

We explore the relationship between Kekulé structures and maximum face independence sets in fullerenes: plane trivalent graphs with pentagonal and hexagonal faces. For the class of leap-frog fullerenes, we show that a maximum face independence set corresponds to a Kekulé structure with a maximum number of benzene rings and may be constructed by partitioning the pentagonal faces into pairs and 3...

Purpose To introduce SHERPA-LEAP, a model for the consortial development, population and support of eprints repositories. Design/methodology/approach The organisational and technical structures of the consortium are described, including a brief summary of central and local resource responsibilities. Some positive and negative aspects of a consortial approach to institutional repository developm...