A Study on One Vertex Union of Alternate Shells Other Labeling in Graph Theory.

Abstract

In this research paper we prove that the one vertex union of alternate shells with a path at any common level with chords ????(2???????? , ???????? − 2, ????, ???????? ), is graceful and admits an ????- valuation, for ???? ≥ 1, ???????? ≥ 3 and 1 − ???? ≤ ????. The graph one vertex union of alternte shells with a path at any common level (with or without chords) ????(2???????? , ???????? − 2, ????, ????), is proved to be cordial, for ???????? = ???? ≥ 3, ???? ≥ 1 and 1 ≤ ???? ≤ ????. As a corollary we also prove that the graph ????(2????, ???? − 2, ????, ????, 2????) is cordial, for ???? ≥ 1, ???? ≥ 3 and 1 ≤ ???? ≤ (???? 1)(???? − 1).