Abstract

New Families of Square Sum Graphs

A. Uma Maheswari1 and V. Srividya*2

1Associate Professor, Department of Mathematics, Quaid-e-Millath Govt College for Women, Chennai-600 106, Tamilnadu, INDIA. 2Associate Professor, Department of Mathematics Bharathi Women’s College, Chennai-600 108, Tamilnadu, INDIA.

ABSTRACT

In this paper Square Sum labeling of new families of graphs using graph operations on cycles with parallel chords are shown with illustrations. We prove that cycles with parallel chords are square sum graphs and extended the result to show that graphs obtained by attaching an arbitrary number of pendant edges at a vertex of degree 2 of cycle with parallel chords, duplication of a vertex of degree 2 of cycle with parallel chords and crown with parallel chords are square sum graphs. We also prove that chain of even cycles with parallel chords, swing with parallel chords are square sum graphs. AMS Subject Classification: 05C78.

Keywords :Square sum labeling, Cycles with parallel chords, Chain of even cycles, Swing of cycles with parallel chords.

map1 map2 map3