Revistas académicas de la Universidad Católica del Norte
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A linear time algorithm for minimum equitable dominating set in trees
No full textLet G = (V, E) be a graph. A subset De of V is said to be an equitable dominating set if for every v ∈ V \ De there exists u ∈ De such that uv ∈ E and |deg(u) − deg(v)| ≤ 1, where, deg(u) and deg(v) denote the degree of the vertices u and v respectively. An equitable dominating set with minimum cardinality is called the minimum equitable dominating set and its cardinality is called the equitable domination number and it is denoted by γe. The problem of finding minimum equitable dominating set in general graphs is NP-complete. In this paper, we give a linear time algorithm to determine minimum equitable dominating set of a tree
The impact of time delay on the transmission of Japanese encephalitis model without vaccination
No full textIn this manuscript, the influence of time delay in the transmission of Japanese encephalitis without vaccination model has been studied. The time delay is because of the existence of an incubation period during which the Japanese encephalitis virus reproduces enough in the mosquitoes with the goal that it tends to be transmitted by the mosquitoes to people. The motivation behind this manuscript is to assess the influence of the time delay it takes to infect susceptible human populations after interacting with infected mosquitoes. The steadystate and the threshold value R0 of the delay model were resolved. This value assists with setting up the circumstance that ensures the asymptotic stability of relating equilibrium points. Utilizing the delay as a bifurcation parameter, we built up the circumstance for the presence of a Hopf bifurcation. Moreover, we infer an express equation to decide the stability and direction of Hopf bifurcation at endemic equilibrium by using center manifold theory and normal structure strategy. It has been seen that delay plays a vital role in stability exchanging. Furthermore, the presence of Hopf bifurcation is affected by larger values of virus transmission rate from an infected mosquito to susceptible individuals and the natural mortality of humans in a model. Finally, to understand some analytical outcomes, the delay framework is simulated numerically
Domination in the entire nilpotent element graph of a module over a commutative ring
No full textLet R be a commutative ring with unity and M be a unitary R module. Let Nil(M) be the set of all nilpotent elements of M. The entire nilpotent element graph of M over R is an undirected graph E(G(M)) with vertex set as M and any two distinct vertices x and y are adjacent if and only if x + y ∈ Nil(M). In this paper we attempt to study the domination in the graph E(G(M)) and investigate the domination number as well as bondage number of E(G(M)) and its induced subgraphs N(G(M)) and Non(G(M)). Some domination parameters of E(G(M)) are also studied. It has been showed that E(G(M)) is excellent, domatically full and well covered under certain conditions
Trees with vertex-edge Roman Domination number twice the domination number minus one
No full textA vertex-edge Roman dominating function (or just ve-RDF) of a graph G = (V, E) is a function f : V (G) → {0, 1, 2} such that for each edge e = uv either max{f (u), f (v)} ≠ 0 or there exists a vertex w such that either wu ∈ E or wv ∈ E and f (w) = 2. The weight of a ve-RDF is the sum of its function values over all vertices. The vertex-edge Roman domination number of a graph G, denoted by γ veR(G), is the minimum weight of a ve-RDF G. We characterize trees with vertexedge roman domination number equal to twice domination number minus one
Creating a new two-step recursive memory method with eight-order based on Kung and Traub's method
No full textWe are devoted to the study of an iterative recursive Traub-Steffensen like method for approximating the simple roots of a nonlinear equation. Using the recursive technique, the R-order of convergence is increased from 4 to 8 without any new function evaluations, which means 100% improvement of the order of the convergence. The theoretical study of the convergence rate is investigated and demonstrated. A few nonlinear problems are presented to justify the theoretical study
A generalization of Fibonacci sequence
No full textWe attempt to generalize Fibonacci sequence by generating certain number of sequences whose terms are obtained by adding the last two generated terms of the preceding sequence. When we consider the particular case of generating only one sequence we obtain the Fibonacci sequence. Moreover we prove some of the results which can be seen as generalized form of the results which hold for Fibonacci sequence. We also verify the results for the particular case of Fibonacci sequence
On the upper geodetic global domination number of a graph
No full textA set S of vertices in a connected graph G = (V, E) is called a geodetic set if every vertex not in S lies on a shortest path between two vertices from S. A set D of vertices in G is called a dominating set of G if every vertex not in D has at least one neighbor in D. A set D is called a global dominating set in G if S is a dominating set of both G and Ḡ. A set S is called a geodetic global dominating set of G if S is both geodetic and global dominating set of G. A geodetic global dominating set S in G is called a minimal geodetic global dominating set if no proper subset of S is itself a geodetic global dominating set in G. The maximum cardinality of a minimal geodetic global dominating set in G is the upper geodetic global domination number Ῡg+(G) of G. In this paper, the upper geodetic global domination number of certain connected graphs are determined and some of the general properties are studied. It is proved that for all positive integers a, b, p where 3 ≤ a ≤ b < p, there exists a connected graph G such that Ῡg(G) = a, Ῡg+(G) = b and |V (G)| = p
On even vertex odd mean labeling of the calendula graphs
No full textA graph G with |E(G)|=q, an injective function f : V (G) → {0, 2, 4, ..., 2q} is an even vertex odd mean labeling of G that induces the values {f(u)+f(v)}/{2} for the q pairs of adjacent vertices u,v are distinct. In this paper, we investigate an even vertex labeling for the calendula graphs. Moreover we introduce the definition of arbitrary calendula graph and prove that the arbitrary calendula graphs are also even vertex odd mean graphs
Independent form of (θ, s)-continuous functions in topological spaces
No full textWe introduce a new class of almost contra-Pβ-continuous functions which is a subclass of the class of almost contra-precontinuous functions [8]. This class contains the classes of regular set connected functions, perfectly continuous functions and contra-Pβ-continuous functions. It is shown that almost contra-Pβ-continuity is independent to (θ, s)-continuity [12] and contra-precontinuity [11]. Furthermore, we obtain basic properties and preservations theorems for almost contra-Pβ-continuity
Distance and eccentricity based polynomials and indices of m-level Wheel graph
No full textDistance and degree based topological polynomial and indices of molecular graphs have various applications in chemistry, computer networking and pharmacy. In this paper, we give hosoya polynomial, Harary polynomial, Schultz polynomial, modified Schultz polynomial, eccentric connectivity polynomial, modified Wiener index, modified hyper Wiener index, generalized Harary index, multiplicative Wiener index, Schultz index, modified Schultz index, eccentric connectivity index of generalized wheel networks Wn,m. We also give pictorial representation of computed topological polynomials and indices on the involved parameters m and n