A graph G of order n is said to be borderenergetic if its energy is equal to 2n-2 and if G differs from the complete graph Kn. The first such graph was discovered in 2001, but their systematic study started only in 2015. Until now, the number of borderenergetic graphs of order n was determined for n

G. Kutty, L. E. Moser, P. M. Melliar-Smith, L. K. Dillon, Y. S. Ramakrishna Department of Electrical and Computer Engineering Department of Computer Science University of California, Santa Barbara, CA 93106 Abstract. Future Interval Logic (FIL) is a linear-time temporal logic that is intended for speci cation and veri cation of reactive and concurrent systems. To make FIL useful for specifying ...

The paper considers the long-time behavior for a class of generalized high-order Kirchhoff-type coupled equations, under corresponding hypothetical conditions, according to Hadamard graph transformation method, obtain equivalent norm in space , and we existence family inertial manifolds while such equations satisfy spectral interval condition.

By developing some new analysis technique, we show that the following discrete single species model with feedback control and time delays is permanent.    N(n + 1) = N(n) exp  r(n) [ 1 − N 2 (n − m) k 2 (n) − c(n)u(n − η) ] , ∆u(n) = −a(n)u(n) + b(n)N(n − σ), where N(n) is the density of species, u(n) is the control variable, ∆ is the first-order forward difference operator ∆u(n) = u(n + 1...

let $g $ be a finite group and let $gamma(g)$ be the prime graph‎ ‎of g‎. ‎assume $2 < q = p^{alpha} < 100$‎. ‎we determine finite groups‎ ‎g such that $gamma(g) = gamma(u_3(q))$ and prove that if $q neq‎ ‎3‎, ‎5‎, ‎9‎, ‎17$‎, ‎then $u_3(q)$ is quasirecognizable by prime graph‎, ‎i.e‎. ‎if $g$ is a finite group with the same prime graph as the‎ ‎finite simple group $u_3(q)$‎, ‎then $g$ has a un...

Given an arbitrary graph G = (V,E) and an interval graph H = (V, F ) with E ⊆ F we say thatH is an interval completion of G. The graphH is called aminimal interval completion of G if, for any sandwich graph H ′ = (V, F ′) with E ⊆ F ′ ⊂ F , H ′ is not an interval graph. In this paper we give a O(nm) time algorithm computing a minimal interval completion of an arbitrary graph. The output is an i...