## Spectra of a New Join in Duplication Graph

**Authors:** K. Reji Kumar, Renny P. Varghese

The Duplication graph DG of a graph G, is obtained by inserting
new vertices corresponding to each vertex of G and making the vertex adja-
cent to the neighbourhood of the corresponding vertex of G and deleting the
edges of G. Let G1 and G2 be two graph with vertex sets V (G1) and V (G2)
respectively. The DG - vertex join of G1 and G2 is denoted by G1 t G2 and
it is the graph obtained from DG1 and G2 by joining every vertex of V (G1)
to every vertex of V (G2). The DG - add vertex join of G1 and G2 is denoted
by G1 ./ G2 and is the graph obtained from DG1 and G2 by joining every
additional vertex of DG1 to every vertex of V (G2). In this paper we determine
the A - spectra and L - spectra of the two new joins of graphs for a regular
graph G1 and an arbitrary graph G2 . As an application we give the number
of spanning tree, the Kirchhoff index and Laplace energy like invariant of the
new join. Also we obtain some infinite family of new class of integral graphs

**Comments:** 10 Pages.

**Download:** **PDF**

### Submission history

[v1] 2016-10-04 22:15:42

**Unique-IP document downloads:** 87 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary.
In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution.
Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*