Graphs satisfying inequality θ(G2)⩽θ(G)

Some Classes of Graphs (dis)satisfying the Zagreb Indices Inequality

Recently Hansen and Vukičević [10] proved that the inequality M1/n ≤ M2/m, where M1 and M2 are the first and second Zagreb indices, holds for chemical graphs, and Vukičević and Graovac [17] proved that this also holds for trees. In both works is given a distinct counterexample for which this inequality is false in general. Here, we present some classes of graphs with prescribed degrees, that sa...

The graphs satisfying conditions of Ore's type

Group connectivity of graphs satisfying Ore-condition

In this paper, we show that a simple graph G satisfying Ore-condition with |V (G)| ≥ 3 is A-connected if and only if G is not a 4-cycle, where A is an abelian group of order at least 4.

On graphs satisfying a strong adacency property

ON GRAPHS SATISFYING A STRONG ADJACENCY PROPERTY Y. Ananchuen and L. Caccetta School of Mathematics and Statistics Curtin University of Technology GPO Box U1987 Perth 6001 Western Australia. Dedicated to the memory of Alan Rahilly, 1947 1992 Let m and n be nonnegative integers and k be a positive integer. A graph G is said to have property P*(m,n,k) if for any set of m + n distinct vertices of ...

2 01 3 Inverse Limit Spaces Satisfying a Poincaré Inequality

We give conditions on Gromov-Hausdorff convergent inverse systems of metric measure graphs which imply that the measured Gromov-Hausdorff limit (equivalently, the inverse limit) is a PI space i.e., it satisfies a doubling condition and a Poincaré inequality in the sense of Heinonen-Koskela [HK96]. The Poincaré inequality is actually of type (1, 1). We also give a systematic construction of exam...