Revistas académicas de la Universidad Católica del Norte
Not a member yet
1687 research outputs found
Sort by
On local antimagic chromatic numbers of circulant graphs join with null graphs or cycles
No full textAn edge labeling of a graph G = (V,E) is said to be local antimagic if there is a bijection f : E → {1,..., |E|} such that for any pair of adjacent vertices x and y, f +(x) ≠ f +(y), where the induced vertex label is f +(x) = ? f(e), with e ranging over all the edges incident to x. The local antimagic chromatic number of G, denoted by χla(G), is the minimum number of distinct induced vertex labels over all local antimagic labelings of G. For a bipartite circulant graph G, it is known that χ(G)=2 but χla(G) ≥ 3. Moreover, χla(Cn ∨ K1)=3 (respectively 4) if n is even (respectively odd). Let G be a graph of order m ≥ 3. In [Affirmative solutions on local antimagic chromatic number, Graphs Combin., 36 (2020), 1337—1354], the authors proved that if m ≡ n (mod 2) with χla(G) = χ(G), m>n ≥ 4 and m ≥ n2/2, then χla(G∨On) = χla(G)+1. In this paper, we show that the conditions can be omitted in obtaining χla(G∨H) for some circulant graph G, and H is a null graph or a cycle. The local antimagic chromatic number of certain wheel related graphs are also obtained
Martingales on principal fiber bundles
No full textLet P(M,G) be a principal fiber bundle, let ω be a connection form on P(M,G), and consider a projectable connection ∇P on P(M,G).
The aim of this work is to determine the ∇P -martingales in P(M,G). Our results allow establishing new characterizations of harmonic maps from Riemannian manifolds to principal fiber bundles
Exponential stability and instability in nonlinear differential equation with multiple delays
No full textInequalities regarding the solutions of the nonlinear differential equation with multiple delays
xl(t) = a(t)f(x(t)) +Σni=1bi(t)f(x(t − hi)),
are obtained by means of Lyapunov functionals. These inequalities are then used to obtain sufficient conditions that guarantee exponential decay of solutions to zero of the multi delay nonlinear differential equation. In addition, we obtain a criterion for the instability of the zero solution. The results generalizes some results in the literature
Existence and uniqueness of the generalized solution of a non-homogeneous hyperbolic differential equation modeling the vibrations of a dissipating elastic rod
No full textThe purpose of this mathematical paper is to establish a qualitative research of the existence and uniqueness of the generalized solution to a non-homogeneous hyperbolic partial differential equation problema
subject to the contour condition u = 0 over Σ, and with initial conditions u(x, 0) = u0(x) in Ω, ∂ut(x, 0) = u1(x) in Ω. In the development of the research, the deductive method of Faedo-Garleskin and Medeiro is used to demonstrate the existence of the generalized solution that consists in the construction of approximate solutions in a finite dimensional space, obtaining a succession of approximate solutions to the non-homogeneous hyperbolic problem, that is, by means of a priori estimations, these successions of approximate solutions are passed to limit in a suitable topology. Then the initial conditions are verified and the uniqueness of the generalized solution is proved
Open global shadow graph and it’s zero forcing number
No full textZero forcing number of a graph is the minimum cardinality of the zero forcing set. A zero forcing set is a set of black vertices of minimum cardinality that can colour the entire graph black using the color change rule: each vertex of G is coloured either white or black, and vertex v is a black vertex and can force a white neighbour only if it has one white neighbour. In this paper we identify a class of graph where the zero forcing number is equal to the minimum rank of the graph and call it as a new class of graph that is open global shadow graph”. Some of the basic properties of open global shadow graph are studied. The zero forcing number of open global shadow graph of a graph with upper and lower bound is obtained. Hence giving the upper and lower bound for the minimum rank of the graph
Properties of nearly S-paracompact spaces
No full textWe study some basic properties of a nearly S-paracompact space and its characterizations under certain hypotheses about space. We establish relationships between this class of spaces and other well-known spaces. Also, we analyze the invariance of nearly S-paracompactness under direct and inverse images of some types of functions
A note on fold thickness of graphs
No full textA 1-fold of G is the graph G0 obtained from a graph G by identifying two nonadjacent vertices in G having at least one common neighbor and reducing the resulting multiple edges to simple edges. A uniform k-folding of a graph G is a sequence of graphs
G = G0, G1, G2,...,Gk, where Gi+1 is a 1-fold of Gi for
i = 0, 1, 2,...,k − 1 such that all graphs in the sequence are singular or all of them are nonsingular. The largest k for which there exists a uniform k- folding of G is called fold thickness of G and this concept was first introduced in [1]. In this paper, we determine fold thickness of corona product graph G ʘ Km , G ʘ S , Kmand graph join G + Km
Quasi-k-normal ring
No full textIn [4] Wei and Libin defined Quasi normal ring. In this paper we attempt to define Quasi-k-normal ring by using the action of k-potent element. A ring is called Quasi-k-normal ring if ae = 0 ⇒ eaRe = 0 for a ∈ N(R)and e ∈ K(R), where K(R) = {e ∈ R|ek = e}. Several analogous results give in [4] is defined here. we find here that a ring is quasi-k-normal if and only if eR(1 − ek−1)Re = 0 for each e ∈ K(R). Also we get a ring is quasi-k-normal ring if and only if Tn(R, R) is quasi-k-normal ring
Study of some algebraic and topological properties of difference gai sequence of interval numbers
No full textHere we have studied some algebraic and topological properties of Difference Gai Sequence of Interval numbers. We study the Completeness, Solidness, Symmetricity and Convergence free
Resistance distance of generalized wheel and dumbbell graph using symmetric {1}-inverse of Laplacian matrix
No full textA new class of graphs called dumbbell graphs, denoted by DB(Wm,n) is the graph obtained from two copies of generalized wheel graph Wm,n, m ≥ 2, n ≥ 3. It is a graph on 2 (m + n) vertices obtained by connecting m-vertices in one copy with the corresponding vertices in the other copy. The resistance distance between two vertices vi and vj, denoted by rij , is defined as the effective electrical resistance between them if each edge of G is replaced by 1 ohm resistor. The Kirchhoff index is the sum of the resistance distances between all pairs of vertices in the graph. In this paper, we formulate the resistance distance of Wm,n and DB(Wm,n) using Symmetric {1}-inverse of Laplacian matrices. We provide examples to illustrate the proposed method and also obtain the Kirchhoff indices for these examples