THE COMPLEMENT METRIC DIMENSION OF GRAPHS AND ITS OPERATIONS
Journal Title: International Journal of Civil Engineering and Technology - Year 2019, Vol 10, Issue 3
Abstract
Let G be a connected graph with vertex set V(G) and edge set E(G). The distance between vertices u and v in G is denoted by d(u, v), which serves as the shortest path length from u to v. Let be an ordered set, and v is a vertex in G. The representation of v with respect to W is an ordered set , | . The set W is called a resolving set for G if each vertex in G has a different representation with respect to W. A resolving set containing minimum cardinality is called a basis for G. The number of vertices in a basis of G is called metric dimension of G, which is denoted by . The is a complement resolving set of G if there are two vertices , such that | | . A complement basis of G is the complement resolving set containing maximum cardinality. The number of vertices in a complement basis of G is called complement metric dimension of G, which is denoted by ̅̅̅̅̅ . In this paper, we examined complement metric dimension of particular graphs and their characteristics. Furthermore, we determined complement metric dimension of corona and comb products graphs.
Authors and Affiliations
L. SUSILOWATI, SLAMIN AND A. ROSFIANA
Keywords
Related Articles
- EP ID EP46808
- DOI -
- Views 204
- Downloads 0
FURTHER ASSESSMENT OF BUCKLING STABILITY OF STEEL PLATES
Thin plates are commonly-used structural members with wide range of applications. In spite of the proliferation of research on the buckling behavior of such members, further detailed investigations are still required f...
LONG-SPAN GLUED WOODEN STRUCTURES AND THEIR USE
To date, glued wooden structures are used in almost all the elements of buildings and structures. Such structures can be found in ceilings, in coatings, beams, trusses, partitions, walls and even in enclosing structure...
ASSESSMENT OF THE OPERATOR'S ABILITY TO PRODUCE QUALITY DRINKING WATER
Refill drinking water depot (DAMIU) is a business that aims to middle and lower class because of its affordable price. The laboratory analysis of refill drinking water quality showed that the total coliform had exceede...
ELEMENT OF RELIGIOSITY PRACTICES AMONG TEENS IN ISLAMIC PERSPECTIVE
This paper focus of social Muslim ummah that different from the generation of prophet Muhammad s.a.w when it comes to observing voluntary worship practices. After prophet Muhammad s.a.w and the following salaf generati...
STUDY ON PERVIOUS CONCRETE
Most cities today are covered with impermeable areas. During heavy rains or floods, water flowing to the surface causes inconvenience to users. In areas with a poor drainage system, this leads to severe flooding in low...