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Abstract
Let and
be two vertex disjoint graphs of orders
and
respectively, where
and
Let
be a specified edge of
such that
is isomorphic to
Let
be a subset of the edge set of
and let
denote the subgraph of
induced by
Let
be the graph obtained by taking one copy of
and
vertex disjoint copies of
and then pasting the edge
in the
th copy of
with the edge
where
Then the copies of the graph
that are pasted to the edges
are called as edge-pockets, and we say
is a graph with
edge-pockets. In this article, we prove some results describing the Laplacian (resp. adjacency) spectrum of
using the Laplacian (resp. adjacency) spectra of
and
The complete Laplacian (resp. adjacency) spectrum of
is also described in some particular cases. As an application, we show that these results enable us to construct infinitely many pairs of Laplacian (resp. adjacency) cospectral graphs.
Acknowledgements
The authors thank the referee and the editor for their comments and suggestions which have helped to improve the manuscript.
Notes
The financial assistance for S. Paul was provided by DST, India, through INSPIRE Fellowship.