Papers by Benjamin Omamalin
The Goldenhar syndrome has been considered for many years to be a polymalformation result of the ... more The Goldenhar syndrome has been considered for many years to be a polymalformation result of the spectrum type, involving structures derived from the first and second pharyngeal arches. It is a rare disease with a prevalence of 1/25 000 born alive but, nevertheless, during the first clinical genetic study of this disability in the Republic of Ecuador, a higher frequency was observed in the whole country. It drew attention that the cases studied showed slight clinical signs that could be undetected and evaluated as an isolated microtia or a congenital deformity generating a hearing disability. Considering the repercussion of the variable signs of this disease, that might be underdiagnosed, a previously validated methodology was applied that allowed a precise diagnosis of the disease to be made. Five cases are presented, three of which have a possible recessive autosomal heritage, while the other two can be considered as new mutations. It is concluded that this syndrome has a highly v...
Discussiones Mathematicae. General Algebra and Applications, 2024
which is also a total dominating set is called a locating total dominating set of G. The minimum ... more which is also a total dominating set is called a locating total dominating set of G. The minimum cardinality of a locating total dominating set of G is called the locating total domination number of G. In this paper, we determine the locating total domination numbers of the join, corona and composition of graphs. Mathematics Subject Classification: 05C69
International Journal of Mathematical Analysis, 2014
Let G = (V (G), E(G)) be a connected graph. A subset S of V (G) is a total dominating set of G if... more Let G = (V (G), E(G)) be a connected graph. A subset S of V (G) is a total dominating set of G if every vertex of G is adjacent to some vertex in S. The set N G (v) is the set of all vertices of G adjacent to v. A subset S of V (G) is a differentiating set of G if N G [u] ∩ S = N G [v] ∩ S for every two distinct vertices u and v in V (G). A differentiating subset S of V (G) which is also a total dominating is called a differentiating total dominating set of G. The minimum cardinality of a differentiating total dominating set of G is called the differentiating total domination number of G. In this paper, we characterize the differentiating total dominating sets in the Cartesian product of graphs. We also determine the relationships between the differentiating total domination number and some other domination number such as domination number, differentiating domination number, and locating total domination number.
Applied Mathematical Sciences, 2014
Let G = (V (G), E(G)) be a connected graph. A subset S of V (G) is a total dominating set of G if... more Let G = (V (G), E(G)) be a connected graph. A subset S of V (G) is a total dominating set of G if every vertex of G is adjacent to some vertex in S. The set N G (v) is the set of all vertices of G adjacent to v. A subset S of V (G) is a locating set of G if N G (u) ∩ S = N G (v) ∩ S for every two distinct vertices u and v in V (G) \ S. A locating subset S of V (G) which is also a total dominating set is called a locating total dominating set of G. The minimum cardinality of a locating total dominating set of G is called the locating total domination number of G. In this paper, we characterize the locating total dominating sets in the Cartesian product of graphs. We also determine the relationships between the locating total domination number and some other domination parameters such as
International Journal of Mathematical Analysis, 2014
Let G = (V (G), E(G)) be a connected graph. A subset S of V (G) is a total dominating set of G if... more Let G = (V (G), E(G)) be a connected graph. A subset S of V (G) is a total dominating set of G if every vertex of G is adjacent to some vertex in S. The set N G [v] is the set of all vertices of G adjacent to v including v. A subset S of V (G) is a differentiating set of G if N G [u]∩S = N G [v]∩S for every two distinct vertices u and v in V (G). A differentiating subset S of V (G) which is also total dominating is called a differentiating total dominating set of G. The minimum cardinality of a differentiating total dominating set of G is called the differentiating total domination number of G. In this paper we characterize the differentiating total dominating sets in the join, corona and composition of graphs.
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Papers by Benjamin Omamalin