Table of Content
Ariel C. Pedrano
Open AccessArticleTribonacci Cordial Labeling of Some Snake Graphs
Ariel C. Pedrano* and Melaine Vieve S. Gudin
Annals of Communications in Mathematics 2025,
8 (3),
393-405
DOI: https://doi.org/10.62072/acm.2025.080306
ABSTRACT. An injective function f : V (G) → {T0, T1, T2, . . . , Tn}, where n = |V (G)| − 1, is said to be a Tribonacci cordial labeling if the induced function f ∗ : E(G) →{0, 1} defined by f∗(uv) = (f(u) + f(v)) mod 2 satisfies the condition |ef (0) − ef (1)| ≤ 1 where ef (0) is the number of edges with label 0 and ef (1) is the number of edges with label 1. A graph that admits a tribonacci cordial labeling is called a Tribonacci cordial graph. In this paper, we determined the Tribonacci Cordial Labeling of Triangular Snake Graph T Sn, Double Triangular Snake Graph D(T Sn), Quadrilateral Snake Graph QSn, Double Quadrilateral Snake Graph D(QSn), and Cycle Quadrilateral Snake Graph C(QSn).
Open AccessArticleOn Pendant Domination Polynomial in the Corona of Some Graphs
Ariel C. Pedrano and Christine R. Giganto
Annals of Communications in Mathematics 2025,
8 (4),
442-450
DOI: https://doi.org/10.62072/acm.2025.080402
ABSTRACT. A dominating set S in G is called a pendant dominating set if ⟨S⟩ contains at least one pendant vertex. The minimum cardinality of a pendant dominating set is called the pendant domination number denoted by γpe(G). The pendant domination polynomial of G is denoted by Dpe(G, x) and is defined as Dpe(G, x) = Pn i=γpe(G) dpe(G, i)x i , where dpe(G, i)x i is the number of pendant dominating sets of size i. In this paper, we obtained the pendant domination number and pendant domination polynomial of the corona of some graphs, namely, Pm ◦ Kn, Cm ◦ Kn and Km ◦ Kn.
Open AccessArticleOn Lucas Cordial Labeling of Some Snake Graphs
Ariel C. Pedrano and Ernesto R. Salise Jr.
Annals of Communications in Mathematics 2025,
8 (4),
451-458
DOI: https://doi.org/10.62072/acm.2025.080403
ABSTRACT. An injective function f : V (G) → {L1, L2, . . . , Ln}, where Lj is the jth Lucas number (j = 1, 2, . . . , n) is said to be Lucas cordial labeling if the induced function f ∗ : E(G) → {0, 1} defined by f ∗(uv) = (f(u) + f(v)) (mod 2) satisfies the condition |ef (0) − ef (1)| ≤ 1, where ef (0) is the number of edges labeled with 0 and ef (1) is the number of edges labeled with 1. A graph which admits Lucas cordial labeling is called Lucas cordial graph.