Michael Jr. Patula BaldadoNegros Oriental State University · Mathematics Department

PH.D. Math

35
Publications
6,564
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63
Citations
Citations since 2017
23 Research Items
56 Citations
Introduction
Skills and Expertise
September 2016 - October 2016
Position
• Acting Dean
Education
June 2006 - March 2011

Publications

Publications (35)
Article
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A nonempty set G is a g-group [with respect to a binary operation ∗] if it satisfies the following properties: (g1) a ∗ (b ∗ c) = (a ∗ b) ∗ c for all a, b, c ∈ G; (g2) for each a ∈ G, there exists an element e ∈ G such that a ∗ e = a = e ∗ a (e is called an identity element of a); and, (g3) for each a ∈ G, there exists an element b ∈ G such that a...
Chapter
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Let XτI be an ideal topological space. A subset A of X is said to be β-open if A⊆clintclA, and it is said to be βI-open if there is a set O∈τ with the property 1O−A∈I and 2A−clintclO∈I. The set A is called βI-compact if every cover of A by βI-open sets has a finite sub-cover. The set A is said to be cβI-compact, if every cover Oλ:λ∈Λ of A by β-open...
Preprint
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Article
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Let G = (V, E) be a graph of order 2n. If A ⊆ V and hAi ∼= hV \Ai, then A is said to be isospectral. If for every n-element subset A of V we have hAi ∼= hV \Ai, then we say that G is spectral-equipartite. In [1], Igor Shparlinski communicated with Bibak et al., proposing a full characterization of spectral-equipartite graphs. In this paper, we gave...
Article
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Let R be a ring with identity 1R. A subset J of R is called a γ-set if for every a ∈ R\J,there exist b, c ∈ J such that a+b = 0 and ac = 1R = ca. A γ-set of minimum cardinality is called a minimum γ-set. In this study, we identified some elements of R that are necessarily in a γ-sets, and we presented a method of constructing a new γ-set. Moreover,...
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Article
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The velocity of a moving object is different when measured from a stationary frame of reference and on a moving frame of reference (see the famous train experiment and the Michelson-Morley experiment). Because velocity is relative to the frame of reference, so do the concepts of "distance" and "time". Thus, were born the concepts of relativistic ma...
Article
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Let X be a topological space and I be an ideal in X. A subset A of a topological space X is called a β-open set if A ⊆ cl(int(cl(A))). A subset A of X is called β-open with respect to the ideal I, or β I-open, if there exists an open set U such that (1) U − A ∈ I, and (2) A − cl(int(cl(U))) ∈ I. A space X is said to be a β I-compact space if it is...
Article
Let X be a topological space and I be an ideal in X. A subset A of a topological space X is called a β-open set if A ⊆ cl(int(cl(A))). A subset A of X is called β-open with respect to the ideal I, or βI -open, if there exists an open set U such that (1) U − A ∈ I, and (2) A − cl(int(cl(U))) ∈ I. A space X is said to be a βI -compact space if it is...
Article
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Let G=(V,E) be a graph. A subset D of G is a p-dominating set of G if |N_G (x)∩D|≥p for all x element of V not in D, where N_G (x) is the set of all vertices which are adjacent to x. The p-domination number of G, denoted by γ_p (G), is the minimum cardinality of a p-dominating sets of G. The p-reinforcement number of G, denoted by r_p(G) , is the m...
Article
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A path P connecting two vertices u and v in a totally colored graph G is called a rainbow total-path between u and v if all elements in V (P) ∪ E(P) , except for u and v, are assigned distinct colors. A total-colored graph is rainbow total- connected if it has a rainbow total-path between every two vertices. The rainbow total-connection number of a...
Article
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Let 𝐺 be a connected simple graph. A nonempty subset 𝑆 of the vertex set 𝑉(𝐺) is a clique in 𝐺 if the graph 〈𝑆 〉 induced by 𝑆 is complete. A clique 𝑆 in 𝐺 is a clique dominating set if it is a dominating set. A clique dominating set 𝑆 is a clique secure dominating set in 𝐺 if for every vertex 𝑢 ∈ 𝑉 𝐺 ∖ 𝑆 , there exists a vertex 𝑣 ∈ 𝑆 ∩ 𝑁𝐺(𝑢), such...
Article
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Let í µí°º = (í µí±(í µí°º), í µí°¸(í µí°º)) be a simple graph. A set í µí± ⊆ í µí±(í µí°º) is called a secure dominating set of a graph í µí°º if for every vertex í µí±¢ ∈ í µí±(í µí°º) ∖ í µí±, there exists í µí±£ ∈ í µí± ∩ í µí± í µí°º (í µí±¢) such that (í µí± ∖ {í µí±£}) ∪ {í µí±¢} is dominating. It is a super secure dominating set if...
Article
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Let f : E(G) → {1, 2, ..., k} be an edge coloring of G, not necessarily proper. A path P in G is called a rainbow path if its edges have distinct colors. A graph G is said to be rainbow-connected, if every two distinct vertices of G is connected by a rainbow path. In this case, we say that f is a rainbow k-coloring of G. The smallest k such that G...
Article
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Let G = (V, E) be a graph. An r-dynamic k-coloring of G is a function f from V to a set C of colors such that (1) f is a proper coloring, and (2) for all vertices v in V, | f (N (v))| ≥ min {r, degG (v)}. The r-dynamic chromatic number of a G, denoted by Xr (G), is the smallest k such that f is an r-dynamic k-coloring of G. This study gave the r-dy...
Poster
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This is the poster for the research entitled Some Topological Classes Arising from gs, m, and n Correspondents presented during the 2016 Annual Convention of the Mathematical Society of the Philippines.
Article
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Article
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In this study, many results about-correspondent,-correspondent, and-correspondent have been established. In particular, the following main results have been generated: (a) the relation R on T(X) given by R if and only if is-correspondent to is an equivalence relation; (b) the relation R on T(X) given by R if and only if is-correspondent to is an eq...
Article
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Let G = (V, E) be a graph and k be a positive integer. A signed qRoman k-dominating function on G is a function f : V → (-1, 1, 2) with the following two properties: (1) f [u]q = Σv∈N(u) f(v) ≥ k for all u ∈ V; and (2) for every v ∈ V with f (v) = -1, there exists w ∈ V with f (w) = 2 such that vw ∈ E. The weight of a signed qRoman k-dominating fun...
Article
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In this study, many results about m-correspondent, n-correspondent, and gs-correspondent have been established. In particular, the following main results have been generated: (a) the relation R on T(X) given by R if and only if is gs-correspondent to is an equivalence relation; (b) the relation R on T(X) given by R if and only if is m-correspondent...
Article
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Let G be a graph. An eternal 1-secure set in a graph G is a set S0 ⊆ V (G) with the property that for any k ε &Ndbl; and any sequence 〈 u1, u2,· · · ·, uk〉 of vertices of G, there exists a sequence 〈 u1, u2,· · · ·, uk〉 of vertices of G with ui ε Si-1 and either ui equal to or adjacent to ui, such that each set Si = (Si-1\{ui}) ∪ {ui} is dominating...
Article
Let (X, t) be topological space. A subset A of X is called a generalized semi-closed set (pure-gsc) set if scl(A) c U whenever A c U and U is open in X [2]. We note that the intersection of two pure-gsc set need not be a pure-gsc set. So that {N: X\N is a pure-gsc set} is not a topology in X. However, if we define a gsc set as an arbitrary intersec...
Article
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Let G = (V,E) be a graph. A set S ⊆ V is a dominating set of G if for every x ∈ V \S, there exists y ∈ 2 S such that xy ∈ E. In this paper, we introduced a new binary graph operation which we call acquiant vertex gluing. Moreover, we gave the domination number of the acquiant vertex gluing of some graphs.
Article
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Article
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Let G be a graph. An eternal 1-secure set in a graph G is a set S 0 ⊆V(G) with the property that for any k∈ℕ and any sequence 〈v 1 ,v 2 ,⋯,v k 〉 of vertices of G, there exists a sequence 〈u 1 ,u 2 ,⋯,u k 〉 of vertices of G with u i ∈S i-1 and either u i equal to or adjacent to v i , such that each set S i =(S i-1 ∖{u i })∪{v i } is dominating in G....

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Projects (5)
Project
Here we are looking for an answer to how information and communication technology affects business. Are there ICT risks and how are they linked to business goal?
Project
The place for conversation about management.
Project
The project aims to produce relevant research connecting graph theory and matrix theory.