### Journals Information

**
Mathematics and Statistics Vol. 8(4), pp. 416 - 423 DOI: 10.13189/ms.2020.080407 Reprint (PDF) (267Kb) **

## 3-Vertex Friendly Index Set of Graphs

**Girija K. P. , Devadas Nayak C ^{*}, Sabitha D’Souza , Pradeep G. Bhat **

Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, India

**ABSTRACT**

Graph labeling is an assignment of integers to the vertices or the edges, or both, subject to certain conditions. In literature we find several labelings such as graceful, harmonious, binary, friendly, cordial, ternary and many more. A friendly labeling is a binary mapping such that where and represents number of vertices labeled by 1 and 0 respectively. For each edge assign the label , then the function f is cordial labeling of G if and , where and are the number of edges labeled 1 and 0 respectively. A friendly index set of a graph is { runs over all f riendly labeling f of G} and it is denoted by FI(G). A mapping is called ternary vertex labeling and represents the vertex label for . In this article, we extend the concept of ternary vertex labeling to 3-vertex friendly labeling and define 3-vertex friendly index set of graphs. The set runs over all 3 ? vertex f riendly labeling f f or all is referred as 3-vertex friendly index set. In order to achieve , number of vertices are partitioned into such that for all with and la- bel the edge by where . In this paper, we study the 3-vertex friendly index sets of some standard graphs such as complete graph K_{n}, path P_{n}, wheel graph W_{n}, complete bipartite graph K_{m,n} and cycle with parallel chords PC_{n}.

**KEYWORDS**

Friendly Labeling, Ternary Vertex Labeling, 3-Vertex Friendly Labeling, 3-Vertex Friendly Index Set

**Cite This Paper in IEEE or APA Citation Styles**

(a). IEEE Format:

[1] Girija K. P. , Devadas Nayak C , Sabitha D’Souza , Pradeep G. Bhat , "3-Vertex Friendly Index Set of Graphs," Mathematics and Statistics, Vol. 8, No. 4, pp. 416 - 423, 2020. DOI: 10.13189/ms.2020.080407.

(b). APA Format:

Girija K. P. , Devadas Nayak C , Sabitha D’Souza , Pradeep G. Bhat (2020). 3-Vertex Friendly Index Set of Graphs. Mathematics and Statistics, 8(4), 416 - 423. DOI: 10.13189/ms.2020.080407.