A bipartite graph G = (L,R;E) where V (G) = L∪R, |L| = p, |R| = q is called a (p, q)-tree if |E(G)| = p+ q − 1 and G has no cycles. A bipartite graph G = (L,R;E) is a subgraph of a bipartite graph H = (L′, R′;E′) if L ⊆ L′, R ⊆ R′ and E ⊆ E′. In this paper we present sufficient degree conditions for a bipartite graph to contain a (p, q)-tree.

In this paper we consider tiling {p, q} of the Euclidean space and of the hyperbolic space, and its dual graph Γ q,p from a combinatorial point of view. A substitution σ q,p on an appropriate finite alphabet is constructed. The homogeneity of graph Γ q,p and its generation function are the basic tools for the construction. The tree associated with substitution σ q,p is a spanning tree of graph ...

the herpesviruses infections in equides are caused by five different serotypes of viruses, belonging to family herpesviridae. the goal of this study was to conduct a seroepidemiological investigation of equine herpesvirus type 1 (ehv-1) and type 4 (ehv-4) in horses and donkeys raised in two provinces and their villages in northeastern turkey. a total of 666 samples from 423 horses and 243 donke...

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Recently, there has been a significant amount of activity to try and understand the discrepancy between Rosenbluth and polarization transfer measurements of the proton form factors. It has been suggested that the standard use of plane-wave Born approximation in extracting the form factors is insufficient, and that higher-order terms must also be included. Of the corrections missing in standard ...

H. K. Nigam and Ajay Sharma Department of Mathematics, Faculty of Engineering & Technology, Mody Institute of Technology and Science (Deemed University), Laxmangarh, Sikar (Rajasthan) 332311, India Correspondence should be addressed to Ajay Sharma, [email protected] Received 7 November 2008; Revised 17 March 2009; Accepted 30 March 2009 Recommended by Hüseyin Bor A new theorem on N...

Let a and b be two positive integers. For the graph G with vertex set V(G) and edge set E(G) with p=IV(G)1 and q=IE(G)I, we define two sets Q(a) and PCb) as follows: Q(a) ={ ± a, ± (a+ 1), ... , ±(a +(q-2)12)} if q is even, Q(a) = (O} u( ± a, ± (a+ 1), ... , ±(a +(q-3)12)} if q is odd, PCb) ={ ± b, ± (b+ I), ... , ±(b +(p-2)/2) l if p is even, PCb) {Ol u( ±b,±(b+l), ... ,±(b+(p-3)12)} ifpisodd....

We prove the exceptional zero conjecture is true for semistable elliptic curves E/Q over number fields of the form F ( e2πi/q n ,∆ 1/q 1 , . . . ,∆ 1/q d ) where F is a totally real field, and the split multiplicative prime p 6= 2 is inert in F (e2πi/q n ) ∩ R. In 1986 Mazur, Tate and Teitelbaum [9] attached a p-adic L-function to an elliptic curve E/Q with split multiplicative reduction at p. ...

In this paper we give all pairs of non mutually placeable (p, q)bipartite graphs G and H such that 2 ≤ p ≤ q, e(H) ≤ p and e(G) + e(H) ≤ 2p+ q − 1.