The energy E(G) of a graph G is equal to the sum of the absolute values of the eigenvalues of G. Several classes of graphs are known that satisfy the condition E(G) > n , where n is the number of vertices. We now show that the same property holds for (i) biregular graphs of degree a b , with q quadrangles, if q<= abn/4 and 5<=a < b = 0 (iii) triregular graphs of degree 1, a, b that are quadran...

expansive soils can be found in many parts of the world particularly in arid and semi-arid regions. these soilspose a significant hazard to civil engineering structures due to its high swelling and shrinkage potential. this paperpresents the results of an experimental program developed to investigate the effect of cyclic drying and wetting on theswelling potential of expansive soils with variou...

A Roman dominating function (RDF) on a graph $G$ is a function $f : V (G) to {0, 1, 2}$satisfying the condition that every vertex $u$ for which $f(u) = 0$ is adjacent to at least onevertex $v$ for which $f(v) = 2$. A Roman dominating function $f$ is called an outer-independentRoman dominating function (OIRDF) on $G$ if the set ${vin Vmid f(v)=0}$ is independent.The (outer-independent) Roman dom...

Let M be a closed orientable 3-manifold of Heegaard genus two with a non-trivial JSJ-decomposition and G be a finite group of orientation-preserving smooth actions on M which preserves each handlebody of Heegaard splitting and each piece of the JSJ-decomposition of M . We will call some specific conditions of the Heegaard splitting and the JSJ-tori the condition A, . . . , and the condition F. ...

‎in this paper we give a new condition for a sylow $p$-subgroup of a finite group to control transfer‎. ‎then it is deduced a characteri-zation of supersoluble groups that can be seen as a generalization of the well known result concerning the supersolubility of finite groups with cyclic sylow subgroups‎. moreover a condition for a normal embedding of a strongly closed $p$-subgroup is given‎. ...

In the present paper, we give a necessary and sufficient condition for a Riemannian manifold (M, g) to have a reducible action of a hyperbolic analogue of the holonomy group. This condition amounts to a decomposition of (M, g) as a warped product of a special form, in analogy to the classical de Rham decomposition theorem for Riemannian manifolds. As a consequence of these results and Berger’s ...

Hall’s condition is a simple condition that a graph G and list assignment L must satisfy if G has a proper L-colouring. The Hall number of G is the smallest integer m such that whenever each list has size m and Hall’s condition is satisfied a proper L-colouring exists. Hilton and P.D. Johnson introduced the parameter and showed that a graph has Hall number 1 if and only if every block is a cliq...

For positive integers d and m, let Pd,m(G) denote the property that between each pair of vertices of the graph G , there are m internally vertex disjoint paths of length at most d. For a positive integer t a graph G satisfies the minimum generalized degree condition δt(G) ≥ s if the cardinality of the union of the neighborhoods of each set of t vertices of G is at least s. Generalized degree co...