, investment officer, First Federal Savings and Loan of Greene County; state Sen. Tim Solobay; John Bendel, director of community investment, Federal Home Loan Bank; Valerie Vicari, director, Division of Western Operations, Pa. Office of Mental Health and Substance Abuse Services; and Greene County Commissioner Chuck Morris.
The 2013 Legislative Luncheon of the Government Affairs Council of the Fayette Chamber of Commerce was an informative and fun event for all.More photographs are available in my photo gallery.
I joined residents, local officials and outdoor enthusiasts to celebrate the receipt of a $120,000 grant that will enable work to begin on a biking and hiking trail linking Point Marion to Morgantown, W.Va., on the Sheepskin Trail. Fayette County and the National Road Heritage Corridor have partnered with elected officials and various organizations to complete the 1.4-mile segment.
A March 1 visit to Graysville Elementary School in the West Greene School District was enjoyed by all. Please check above the Read Across America photo gallery for more pictures.
It was an honor to help celebrate the 99th birthday of Hazel O'Donnell at her Waynesburg home on Feb. 18. I was very pleased to be able to present her with a citation from the House of Representatives.
Rep. Snyder reacts to Gov. Corbett's budget proposal.
State Rep. Pam Snyder is congratulated by Democratic Leader Frank Dermody moments after they were sworn in Jan. 1, 2013, to the 197th session of the Pa. House of Representatives.
State Rep. Pam Snyder, a former Greene County commissioner, is joined by family and friends after she took the oath of office for her first term in the state House.
State Rep. Pam Snyder congratulates fellow, incoming lawmakers, Rep. Patty Kim (center) and Rep. Mary Jo Daley, during swearing in ceremonies.
Rep. Snyder speaks at a news conference calling for a renewed commitment to repeal changes made to Pennsylvania’s Small Games of Chance Act, which is set to take effect in February 2013. More photos from the event can be seen in her galleries section.How Not to Get Stung By Bees
It is no secret that the author of this article is a big fan of honeybees and bumblebees, and an unabashed promoter of bee-friendly landscaping. Honeybees, by eating other insect pests. However, they're aggressive enough that most university extension services recommend having their nests removed by a qualified pest control expert.
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Avoid stings from honeybees and bumblebees
Although honeybees and bumblebees are animals that you actually want in your garden, they do sting if provoked. Avoid being stung by taking a few simple actions, as recommended by the University of Maine Cooperative Extension:
- Cover as much of your body as you can with light-colored, smooth-finished clothing (this also prevents sunburn when working in the garden).
- Keep your yard free of sugary garbage, such as remnants of soda from a barbecue.
- If you see a bee, don't swat at it. Remain still, and the honeybee or bumblebee will probably fly away. Swatting at the bee will increase the likelihood of it stinging you.
- Wear shoes or sandals while playing or working outside. Every bee sting I have received happened because I stepped on a bee while walking barefoot in the grass, so wearing footwear outdoors is a very simple way to avoid a painful bee sting on the bottom of the foot.
- Should you get swarmed by bees, don't run, as running will attract more. Instead, seek shelter indoors. If you are outside, move to a shaded area to get away from the bees.
Needless to say, if you are allergic to bees, always carry an allergy kit with you, and know how to use it.
Treat a bee sting
- If you do get stung by a honeybee, you'll need to remove the stinger. The Indianapolis-area pest control experts at Purdue University recommend that you.
Chaya Kurtz writes for Networx.com.
Updated April 4, 2018.
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The matching polynomials and spectral radii of uniform supertrees

We study matching polynomials of uniform hypergraph and spectral radii of uniform supertrees. By comparing the matching polynomials of supertrees, we extend Li and Feng's results on grafting operations on graphs to supertrees. Using the methods of grafting operations on supertrees and comparing matching polynomials of supertrees, we determine the first $\lfloor\frac{d}{2}\rfloor+1$ largest spectral radii of $r$-uniform supertrees with size $m$ and diameter $d$. In addition, the first two smallest spectral radii of supertrees with size $m$ are determined.


Introduction
The ordering of graphs by spectral radius was proposed by Collatz and Sinogowitz [7] in 1957. Lovász and Pelikán [21] investigated the spectral radius of trees and determined the first two largest and smallest spectral radii of trees with given order. Brualdi and Solheid [2] proposed the problem of bounding the spectral radius of some class of graphs and characterizing the corresponding extremal graphs. Since then, many authors studied the spectral radius of trees with some given parameters, such as degree, diameter, etc.
A hypergraph H is a pair (V, E), where E ⊆ P(V ) and P(V ) stands for the power set of V.
The elements of V = V (H) are referred to as vertices and the elements of E = E(H) are called hyperedges or edges. A hypergraph H is r-uniform if every edge e ∈ E(H) contains precisely r vertices. For a vertex v ∈ V, we denote by E v the set of edges containing v. The cardinality |E v | is the degree of v, denoted by deg (v). A vertex with degree one is called a core vertex, and a vertex with degree larger than one is called an intersection vertex. If any two edges in H share at most one vertex, then H is said to be a linear hypergraph. In this paper we assume that hypergraphs are linear and r-uniform.
In a hypergraph H, two vertices u and v are adjacent if there is an edge e of H such that {u, v} ⊆ e. A vertex v is said to be incident to an edge e if v ∈ e. A walk of hypergraph H is defined to be an alternating sequence of vertices and edges v 1 e 1 v 2 e 2 · · · v e v +1 satisfying that both In [16] some transformations on hypergraphs such as moving edges and edge-releasing were introduced and the first two spectral radii of supertrees on n vertices were characterized. Yuan et.
al [32] further determined the first eight uniform supertrees on n vertices with the largest spectral radii. Xiao et. al [27] characterized the unique uniform supertree with the maximum spectral radius among all uniform supertrees with a given degree sequence. Recently, the first two largest spectral radii of uniform supertrees with given diameter were characterized in [28].
In this paper, we determine the first d 2 + 1 largest spectral radii of supertrees among all runiform supertrees with size m and diameter d and the first two smallest spectral radii of supertrees with size m. The structure of the remaining part of the paper is as follows: In Section 2, we give some basic definitions and results for tensor and spectra of hypergraphs. Section 3 extends the theory of matching polynomial from graphs to supertrees. By comparing the matching polynomial of supertrees, we generalize Li and Feng's results on grafting operations on graphs to supertrees in Section 4. By using the method of grafting operations on supertrees and comparing matching polynomial of supertrees, we determine the first d 2 + 1 spectral radii of supertrees among all runiform supertrees with size m and diameter d in Section 5. In Section 6, the first two smallest spectral radii of supertrees are determined. We give closing remarks in the last section.

Preliminaries
Let H = (V, E) be an r-uniform hypergraph on n vertices. A partial hypergraph H = (V, E ) of H is a hypergraph with V ⊆ V and E ⊆ E. A proper partial hypergraph H of H is partial hypergraph Let G = (V, E) be an ordinary graph. For every r ≥ 3, the rth power of G, denoted by G r, is an r-uniform hypergraph with vertex set V (G r ) = V ∪ (∪ e∈E {i e,1,..., i e,r−2 }) and edge set E(G r ) = {e ∪ {i e,1,..., i e,r−2, }| e ∈ E}. The rth power of an ordinary tree is called a hypertree (see [14]). Note that all hypertrees are supertrees by the definition. Let P m and S m denote the path and the star with m edges, respectively. The rth power of P m and S m, denoted by P r m and S r m, are called loose path and hyperstar, respectively.
Let H = (V, E) be an r-uniform hypergraph. An edge e is called a pendent edge if e