Odd and even repetition sequences of independent domination number

2021

JFMA

Section: Pendahuluanmentioning

confidence: 99%

A Short Note on Fibonacci Numbers in a Generalized Pythagorean Triples

2021

JFMA

“…The smallest cardinality of a dominating set is called dominating number of graph denoted by ( ). Domination concepts in graphs and some of its variants can be found in [4] , where is the triangular number in graph [13] [2] [14]. The minimum cardinality of a secure dominating set of , denoted by ( ) is called a secure domination number of .…”

Section: Abstrak Misalmentioning

confidence: 99%

On Triangular Secure Domination Number

InPrime:Ind.Jour.Pure.Applied.Math

Valenzona

et al. 2020

Let T_m=(V(T_m), E(T_m)) be a triangular grid graph of m ϵ N level. The order of graph T_m is called a triangular number. A subset T of V(T_m) is a dominating set of T_m if for all u_V(T_m)\T, there exists vϵT such that uv ϵ E(T_m), that is, N[T]=V(T_m). A dominating set T of V(T_m) is a secure dominating set of T_m if for each u ϵ V(T_m)\T, there exists v ϵ T such that uv ϵ E(T_m) and the set (T\{u})ꓴ{v} is a dominating set of T_m. The minimum cardinality of a secure dominating set of T_m, denoted by γ_s(T_m) is called a secure domination number of graph T_m. A secure dominating number γ_s(T_m) of graph T_m is a triangular secure domination number if γ_s(T_m) is a triangular number. In this paper, a combinatorial formula for triangular secure domination number of graph T_m was constructed. Furthermore, the said number was evaluated in relation to perfect numbers.

“…For other concepts of graph theory, readers may refer to the following references [7][8][9][10][11][12][13]. We also introduce a new graph in this paper, that is, the H graph.…”

Section: Introductionmentioning

confidence: 99%

On Even-to-Odd Mean Labeling of Some Trees

2021

JFMA

Let G=(V(G), E(G)) be a connected graph with order |V(G)|=p and size |E(G)|=q. A graph G is said to be even-to-odd mean graph if there exists a bijection function phi:V(G) to {2, 4, ..., 2p} such that the induced mapping phi^*:E(G) to {3, 5, ..., 2p-1} defined by phi^*(uv)=[phi(u)+phi(v)]/2 for all uv element of E(G) is also bijective. The function is called an even-to-odd mean labeling of graph . This paper aimed to introduce a new technique in graph labeling. Hence, the concepts of even-to-odd mean labeling has been evaluated for some trees. In addition, we examined some properties of tree graphs that admits even-to-odd mean labeling and discussed some important results.