Revistas académicas de la Universidad Católica del Norte
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Tight Bounds for the N₂-Chromatic Number of Graphs
No full textLet be a connected graph. A vertex coloring of is an -vertex coloring if, for every vertex , the number of different colors assigned to the vertices adjacent to is at most two. The -chromatic number of is the maximum number of colors that can be used in an -vertex coloring of . In this paper, we establish tight bounds for the -chromatic number of a graph in terms of its maximum degree and its diameter, and characterize those graphs that attain these bounds
Further results on edge irregularity strength of some graphs
No full textThe focal point of this paper is to precisely ascertain the edge irregularity strength of various finite, simple, and undirected captivating graphs, including splitting graph, shadow graph, jewel graph, jellyfish graph, and copies of 4-pan graph
On graded 1 -absorbing δ -primary ideals
No full textLet G be an abelian group with identity 0 and let R be a commutative graded ring of type G with nonzero unity. Let I(R) be the set of all ideals of R and let δ: I(R)⟶I(R) be a function. Then, according to (R. Abu-Dawwas, M. Refai, Graded δ-Primary Structures, Bol. Soc. Paran. Mat., 40 (2022), 1-11), δ is called a graded ideal expansion of a graded ring R if it assigns to every graded ideal I of R another graded ideal δ(I) of R with I ⊆ δ(I), and if whenever I and J are graded ideals of R with J ⊆ I, we have δ (J) ⊆ δ(I). Let δ be a graded ideal expansion of a graded ring R. In this paper, we introduce and investigate a new class of graded ideals that is closely related to the class of graded δ-primary ideals. A proper graded ideal I of R is said to be a graded 1-absorbing δ-primary ideal if whenever nonunit homogeneous elements a,b,c ∊ R with abc ∊ I, then ab ∊ I or c ∊ δ(I). After giving some basic properties of this new class of graded ideals, we generalize a number of results about 1-absorbing δ-primary ideals into these new graded structure. Finally, we study the graded 1-absorbing δ-primary ideals of the localization of graded rings and of the trivial graded ring extensions
Split domsaturation and Some New Parameters
No full textLet G be any connected graph. The split domination number γs (G) of G is the minimum cardinality of a split dominating set. The split domsaturation number
dss (G) of a graph G is the least positive integer k such that every vertex of G lies in a split dominating set of cardinality k. A split dominating set S ⊆ V (G) is said to be connected split dominating set if < S > is connected. The minimum cardinality of all connected split dominating sets of G is called the connected split omination number of G and is denoted by γcs (G). The uniform split domination number γus (G) of a graph G is the least positive integer k, such that every k-element split subset S of V is a dominating set in G. In this paper, we investigate several properties of these dominating sets
The character table of a subgroup of
No full textThe symplectic group has a unique absolutely irreducible module of dimension 16 over . Hence a split extension group of the form exists. The structure of the group makes it most suitable for a standard application of the Fischer-Clifford matrices technique to compute its ordinary character table. Since this is a very large group it will not be possible to compute its character table in GAP or MAGMA with an average computer device. An existing GAP routine which computes candidates for the Fischer-Clifford matrices of an extension group, such as , also fails. This makes a very interesting group for an application of the Fischer-Clifford matrices technique. In this paper, the authors use mostly brute force and some GAP subroutines to construct the Fischer-Clifford matrices and ordinary character table of
Pairwise Infra Neutrosophic Pre-Open Set in Infra Neutrosophic Bi-topological Space
No full textIn this article, we present the notion of infra neutrosophic bi-topological spaces (in short INBTS) as a generalization of infra neutrosophic topological space (in short INTS) and neutrosophic bi-topological space (in short NBTS). Besides, we study the different types of open and closed sets namely infra neutrosophic bi-open set (in short INBOS), infra neutrosophic bi-semi-open set (in short INBSOS), infra neutrosophic bi-pre-open set (in short INBPOS), infra neutrosophic bi-b-open set (in short INBb-OS), etc. via INBTSs. Then, we introduce the notion of pairwise infra neutrosophic bi-open set (in short PINBOS), pairwise infra neutrosophic bi-semi-open set (in short PINBSOS), pairwise infra neutrosophic bi-pre-open set (in short PINBPOS), pairwise infra neutrosophic bi-b-open set (in short PINBb-OS), and furnish few illustrative examples on them. Further, we investigate several properties of these classes of sets and establish several interesting results via INBTSs in the form of propositions, theorems, etc
Maximal graphical realization of a topology
No full textGiven a topological space, the graphical realizations of it with as many edges as possible, called maximal graphical realizations, are studied here. Every finite topological space admits a maximal graphical realization. However, there are graphs which are not maximal graphical realizations of any topology. A tree of odd order is never a maximal graphical realization of a topological space. Maximal graphical realization of a topology is a cycle if and only if it is C_3. It is shown that chain topologies admit unique maximal graphical realizations. A lower bound for the size of a maximal graphical realization is also obtained
On edge irregularity strength of cycle-star graphs
No full textFor a simple graph G, a vertex labeling ϕ : V (G) → {1, 2, . . . , k} is called k-labeling. The weight of an edge uv in G, written wϕ(uv), is the sum of the labels of end vertices u and v, i.e., wϕ(uv) = ϕ(u) + ϕ(v). A vertex k-labeling is defined to be an edge irregular k-labeling of the graph G if for every two distinct edges u and v, wϕ(u) ̸= wϕ(v). The minimum k for which the graph G has an edge irregular k-labeling is called the edge irregularity strength of G, written es(G). In this paper, we study the edge irregular k-labeling for cycle-star graph CSk,n−k and determine the exact value for cycle-star graph for 3 ≤ k ≤ 7 and n − k ≥ 1. Finally, we make a conjecture for the edge irregularity strength of CSk,n−k for k ≥ 8 and n − k ≥ 1
Pringsheim and lacunary -statistical convergence for double sequence on fuzzy normed space
No full textWe explore the idea of lacunary -statistical convergence for double sequences on -fuzzy normed spaces. Then, we provide a useful characterization of the lacunary -statistical convergence of double sequences with respect to their convergence in the classical sense and show how our method of convergence is weaker than the usual convergence for double sequences on -fuzzy normed spaces. Towards the end, we give the novel relation between lacunary -statistical cauchy sequence and lacunary -statistical bounded double sequence
The Cordial Energy of Some Graphs
No full textThis paper provides a comprehensive investigation into cordial spectra and energy. The study delves into the fundamental principles of cordial labeling, where graph vertices are assigned labels to maintain balanced adjacency. The analysis includes mathematical properties and the interplay between cordial labeling and graph energy. Spectral analysis involving eigenvalues of matrices associated with cordially labeled graphs is explored, offering insights into graph structural characteristics and relationships