One Edge Union of \(k\) Shell Graphs is Cordial

Abstract

A shell graph of order \(n\), denoted by \(H(n, n-3)\), is the graph obtained from the cycle \(C_n\) of order \(n\) by adding \(n-3\) chords incident with a common vertex, say \(u\). Let \(v\) be a vertex adjacent to \(u\) in \(C_n\). Sethuraman and Selvaraju \([3]\) conjectured that for all \(k \geq 1\) and for all \(n_i \geq 4\), \(1 \leq i \leq k\), one edge \((uv)\) union of \(k\)-shell graphs \(H(n_i, n_i – 3)\) is cordial. In this paper, we settle this conjecture affirmatively.