**InternationaleJournals**

**On
New Vertex Naturally Labeled Graphs**

**M.A.Rajan ^{*}, V. Lokesha^{**},
Ranjini P.S^{***}**

^{*}*Innovation Labs,
Tata consultancy Services Limited, **Bangalore, India,*

***Department of Mathematics, Acharya Institute of Technology, Bangalore-90,Karnataka,India*

****Department of mathematics, Don Bosco Institute of
Technology, Bangalore-74, Karnataka, India*

*email: *^{*}*rajan.ma@tcs.com ,*^{ **}*lokeshav@acharya.ac.in,*^{ ***}*ranjini_p_s@yahoo.com*

**Abstract**

Vertices of the graphs are labeled from the set of natural numbers from one to the order of the given graph. Vertex Adjacency Label Set(VALS) is the set of ordered pair of vertices and its corresponding label of the graph. In this paper we introduced a notion of Vertex Adjacency Label Number(VALN). For each VALS, VLN of graph is the sum of labels of all the adjacent pairs of the vertices of the graph. is the maximum number among all the VALNs of the different labeling of the graph and the corresponding VALS is defined as Max Vertex Adjacency Label Set . In this paper for special graphs are computed and also algorithm to find the of any graph is described.

**Subject
Classification**:* 05C12, 05C07*

**Key Words**: Graph
labeling, Graceful labeling, Complement

**International
eJournal of Mathematics and Engineering**

**Volume** 2,
**Issue** 2, **Pages**: 992 - 999