In the wheel the vertex corresponding to is called the apex vertex and the vertices corresponding to are called the rim vertices. Vaidya, S. But in the following theorem we have proved that is switching invariant if is even. Case 4: If thenfor. Figure 4. A necessary and sufficient condition for the complement of to be a prime graph is investigated. Definition 1. Thus and the graph obtained by switching any vertex of are prime graphs. Deretsky et al. If then and.

PDF | A graph G = (V, E) with n vertices is said to admit prime labeling if its Deﬁnition A prime labeling of a graph G is an injective function f: V →{1, 2, they present the neighborhood-prime labeling of G B * B, where B is the book with. in which adjacent vertices are given relatively prime labels, and a graph.

## Some Results on Prime Labeling

is prime if the We then deﬁne pr(G) to be the minimum value of kfor. A graph admitting a prime labeling is called a prime graph.

Example we can define an injective function f: V--> 11, 2, n} such that f(B) c {1} u P(n12. Now we take up the graph B = Kim x P2, called a book.

Theorem.

Figure 1. So in every vertex other than and is adjacent to and only. Vaidya 1Udayan M.

### Some Switching Invariant Prime Graphs

Open Journal of Discrete Mathematics, 2, Thus and the graph obtained by switching of any vertex in are prime graphs. Hence the result.

Video: Prime label definition book PLR books (Private Label Rights) for books and ebooks or white label licensing for books

CANCERIANS COMPATIBILITY WITH SAGITTARIUS |
Proof : Let be consecutive rim vertices of and be the apex vertex of. Lee [6] that wheel graph is a prime graph if and only if is even. We noticed that it is not easy to discuss the prime labeling of a graph obtained by switching any rim vertex of when is a composite number.
Many researchers have studied prime graphs. So we have to use 1 to natural numbers to label these vertices, and from 1 to there are even integers. Proof: Let be the vertex of and be the vertices of copy of cycle where. |

1. Definition An independent set of vertices in a graph is a set of. stars, cycle chains, prisms, and generalized books.

## Primary Label is defined here as a labelling term. Primary Label Labelplanet

1. Introduction All unicyclic graphs have a prime vertex labeling (Seoud and Youssef [5]). classes of graphs such as polygonal snakes and books, with a focus on trees including caterpillars, neighborhood-prime labeling of a graph G with n vertices is a labeling of the vertex set with We define a labeling for the.

Therefore the remaining vertices forms a path in and these vertices will receive.

Thus maximum three vertices can be labeled as even number. Let be the vertex set of then. The notion of prime labeling was originated by Entringer and was discussed in A. For various graph theoretic notations and terminology we follow Gross and Yellen [1] whereas for number theory we follow D.

Proof: In the prism graph there are two cycles. Vaidya, S.

Also are the vertices of. Received November 12, ; revised December 10, ; accepted December 31,

The prime labeling of the graph obtained by switching a pendant vertex of.

It can be easily verified that is a prime labeling.