Michael Jr. Patula Baldado

Negros Oriental State University · Mathematics Department

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...

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...

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...

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,...

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...

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...

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...

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...

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...

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...

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...

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...

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...

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.

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...

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...

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...

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...

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...

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.

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....