Total Perfect Hop Domination in Graphs Under Some Binary Operations

被引：3

作者：

Rakim, Raicah C. ^{[1
]}

Rara, Helen M. ^{[1
]}

机构：

[1] Mindanao State Univ, Coll Nat Sci & Math, Math Dept, Main Campus, Marawi City 9700, Philippines

来源：

EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS | 2021年 / 14卷 / 03期

关键词：

total perfect hop domination; total perfect point-wise non-domination; perfect total (1; 2)*-domination; join; corona; lexicographic product;

D O I：

10.29020/nybg.ejpam.v14i3.3975

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G = (V(G), E (G)) be a simple graph. A set S subset of V(G) is a perfect hop dominating set of G if for every v is an element of V(G) \ S, there is exactly one vertex u is an element of S such that d(G)(u, v) = 2. The smallest cardinality of a perfect hop dominating set of G is called the perfect hop domination number of G, denoted by gamma(ph)(G). A perfect hop dominating set S subset of V(G) is called a total perfect hop dominating set of G if for every v is an element of V(G), there is exactly one vertex u is an element of S such that d(G)(u, v) = 2. The total perfect hop domination number of G, denoted by gamma(tph)(G), is the smallest cardinality of a total perfect hop dominating set of G. Any total perfect hop dominating set of G of cardinality gamma(tph)(G) is referred to as a gamma(tph)-set of G. In this paper, we characterize the total perfect hop dominating sets in the join, corona and lexicographic product of graphs and determine their corresponding total perfect hop domination number.

引用

页码：803 / 815

页数：13

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