SOME POLYNOMIALS AND RESULTS ON DEFICIENT DEGREE OF VERTEX IN STACKED BOOK GRAPH
By
Ravi Ratn Gaur and Pravin Garg
Department of Mathematics University of Rajasthan, Jaipur, Rajasthan, India-302004
Email: ravig2016uor@gmail.com,garg.pravin@gmail.com
(Received: June 19, 2025; In format: August 22, 2025; Revised: November 25, 2025; Accepted: November 26, 2025)
DOI: https://doi.org/10.58250/jnanabha.2025.55226
Abstract
The degree d(v) of a vertex v in a graph G has several fundamental applications in graph theory. A new version of the degree of a vertex v in the graph G is defined as df(v) = ∆ (G) − d (v), where ∆ (G) = max {d(v)|v ∈ V(G)}. Further, we found some results on this new degree of a vertex in the graph G called “deficient degree”. The main object of this article is to study the new version of the polynomial for the stacked book graph as deficient degree vertex polynomial, nbd deficient degree vertex polynomial, deficient M-polynomial, and nbd deficient M-polynomial.
2020 Mathematical Sciences Classification: 05C07, 05C09, 05C31
Keywords and Phrases: Deficient degree, vertex polynomial, neighborhood vertex polynomial, M-polynomial and neighborhood M-polynomial, stacked book graph.