A 2-edge-covering between G and H is an onto homomorphism from the vertices of G to the vertices of H so that each edge is covered twice and edges in H can be lifted back to edges in G. In this note we show how to compute the spectrum of G by computing the spectrum of two smaller graphs, namely a (modified) form of the covered graph H and another graph which we term the anti-cover. This is done...

A very well–covered graph is an unmixed without isolated vertices such that the height of its edge ideal half number vertices. We study these graphs by means Betti splittings and mapping cone constructions. show cover ideals Cohen–Macaulay are splittable. As a consequence, we compute explicitly minimal graded free resolution class prove have homological linear quotients. Finally, conjecture sam...

We consider n independent points with a common but arbitrary density fin R a. Two points (X~, Xj) are joined by an edge when a certain set S(X~, Xj) does not contain any other data points. The expected number E(N) of edges in the graph depends upon n, f and the definition of S. Examples include rectangles, spheres and loons; these lead to the graph of all dominance pairs, the Gabriel graph and ...

A path-factor is a spanning subgraph F of G such that every component path with at least two vertices. Let k ? 2 be an integer. P -factor means factor in which each graph covered if for any e ? E ( ), has covering . called uniform 1 , ) ? and avoiding In other words, ? graph. this paper, we present sufficient conditions graphs to ?3 depending on binding number degree conditions. Furthermore, sh...

this survery investigated the secondary school students attitude regarding parent- adolescent inter-relationships. the study covered 19 town districts in tehran.   following a multi-stage process 150 girls and boys attending secondary school with an age range of 13-15 years were selected randomly.   a two parts questionnaire was developed. the first part covered information on personal and soci...

A P ≥ k -factor of a graph G is spanning subgraph whose components are paths order at least . We say that covered if for every edge e ∈ E ( ), admits contains ; and we uniform the − covered. In other words, pair edges 1 , 2 avoids this article, testify (1) 3-edge-connected its isolated toughness I ) > 1; (2) 2. Furthermore, explain these conditions on edge-connectivity in our main results be...

Let K be a field and let $$S=K[x_1,\ldots ,x_n]$$ standard polynomial ring over K. We characterize the extremal Betti numbers, values as well positions, of t-spread strongly stable ideal S. Our approach is constructive. Indeed, given some positive integers $$a_1,\dots ,a_r$$ pairs $$(k_1,\ell _1),\ldots ,(k_r,\ell _r)$$ , we are able to determine under which conditions there exists I S with $$\...

Rats and mice were studied for changes in meal-taking structure in a closed operant food economy, in which the consummatory or unit prices for food were increased. In experiment 1, as food price increased, male rats modestly decreased the number of meals per day and increased mean meal size. Female rats were similar to males but had smaller meal size and, at low costs, took more meals per day. ...

Evaluation of ecosystem services has become a hotspot in terms of research focus, but uncertainties over appropriate methods remain. Evaluation can be based on the unit price of services (services value method) or the unit price of the area (area value method). The former takes meteorological factors into account, while the latter does not. This study uses Kunyu Mountain Nature Reserve as a stu...

The boxicity box(H) of a graph H is the smallest integer d such that H is the intersection of d interval graphs, or equivalently, that H is the intersection graph of axis-aligned boxes in R. These intersection representations can be interpreted as covering representations of the complement H of H with co-interval graphs, that is, complements of interval graphs. We follow the recent framework of...