On the gracefulness of m-super subdivision of graphs

Venkatesh Srinivasan1 Department of Mathematics, Srinivasa Ramanujan Centre, SASTRA Deemed University, Kumbakonam612001, Tamil Nadu, India E-mail: [email protected]

Natarajan Chidambaram2 Department of Mathematics, Srinivasa Ramanujan Centre, SASTRA Deemed University, Kumbakonam612001, Tamil Nadu, India E-mail: [email protected]

Narasimhan Devadoss3 Department of Mathematics, Srinivasa Ramanujan Centre, SASTRA Deemed University, Kumbakonam612001, Tamil Nadu, India E-mail: [email protected]

Rajadurai Pakkirisamy4 Department of Mathematics, Srinivasa Ramanujan Centre, SASTRA Deemed University, Kumbakonam612001, Tamil Nadu, IndiaCorrespondence[email protected]

Parameswari Krishnamoorthi5 Department of Mathematics, Srinivasa Ramanujan Centre, SASTRA Deemed University, Kumbakonam612001, Tamil Nadu, India E-mail: [email protected]

Abstract

Let G be a connected simple graph. A graph H is said to be a m-Super subdivision of G, if every edge of G is replaced by the complete bipartite graph K_m,m with m > 2 in such a way that the end vertices of the edge are merged with any two vertices of the same partite set A or B of K_m,m after removal of the edge of G. In this paper, we prove that m-Super subdivision of path and cycle are graceful.

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