Let H be a graph and t ≥ s ≥ 2 be integers. We prove that if G is an n-vertex graph with no copy of H and no induced copy of Ks,t, then λ(G) = O ( n1−1/s ) where λ(G) is the spectral radius of the adjacency matrix of G. Our results are motivated by results of Babai, Guiduli, and Nikiforov bounding the maximum spectral radius of a graph with no copy (not necessarily induced) of Ks,t.

Let G be a random subgraph of the n-cube where each edge appears randomly and independently with probability p. We prove that the largest eigenvalue of the adjacency matrix of G is almost surely λ1(G) = (1 + o(1))max ( ∆(G), np ) , where ∆(G) is the maximum degree of G and the o(1) term tends to zero as max(∆(G), np) tends to infinity.

In this article we discuss a data structure, which combines advantages of two different ways for representing graphs: adjacency matrix and collection of adjacency lists. This data structure can fast add and search edges (advantages of adjacency matrix), use linear amount of memory, let to obtain adjacency list for certain vertex (advantages of collection of adjacency lists). Basic knowledge of ...

In this paper those graphs are studied for which a so-called strong ordering of the vertex set exists. This class of graphs, called strongly orderable graphs, generalizes the strongly chordal graphs and the chordal bipartite graphs in a quite natural way. We consider two characteristic elimination orderings for strongly orderable graphs, one on the vertex set and the second on the edge set, and...

The world’s attention has turned towards renewable energy due to escalating demands, declining fossil fuel reservoirs, greenhouse gas emissions, and the unreliability of conventional systems. sun is only source that available every day for a specific period time. Solar photovoltaic (PV) technology known its direct conversion sunlight into electricity using photoelectric effect. However, non-lin...

Excessive ordering of blood components causes problems such as a lack proper distribution products between centers, increased costs, and workload banks. Effective use MSBOS will reduce the cross-match patient samples unnecessary testing. This is also expected way to improve quality health services at UNAIR Hospital treatment costs. study aimed find out profile for orthopedic surgery in period J...

A necessary and sufficient condition for a preference ordering defined on a chain-complete poset to attain its maximum in every subcomplete chain is obtained. A meet-superextremal, or join-superextremal, function on a complete lattice attains its maximum in every subcomplete sublattice if and only if it attains a maximum in every subcomplete chain.

In this paper we prove some stochastic comparisons results for progressive type II censored order statistics. The problem of stochastically comparing concomitants of the two progressive type II censored order statistics with possibly different schemes, under different kinds of dependence between X and Y is considered and it is proved that if Y is stochastically increasing (decreasing) in X, ...

Aim Inventorying plant species in an area based on randomly placed quadrats can be quite inefficient. The aim of this paper is to test whether plant species richness can be inventoried more efficiently by means of a spectrally-based ordering of sites to be sampled. Location The study area was a complex wetland ecosystem, the Lake Montepulciano Nature Reserve, central Italy. This is one of the m...