Some analysis on the geodesic polynomial of graphs and its vertex

Pattanaik, Bijayani; Behera, Amiya Kumar

doi:10.47974/JDMSC-2404

Open Access Research Article

Some analysis on the geodesic polynomial of graphs and its vertex

Bijayani Pattanaikbijayanipattanaik27@gmail.comDepartment of Mathematics Siksha ‘O’ Anusandhan (Deemed to be University)Bhubaneswar, Odisha, 751030, IndiaView full profile → , ^*Amiya Kumar BeheraCorresponding authoramiyabehera@soa.ac.inDepartment of Mathematics Siksha ‘O’ Anusandhan (Deemed to be University)Bhubaneswar, Odisha, 751030, IndiaView full profile →

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pp. 2251–2259Vol. 29Issue 6June 2026DOI: 10.47974/JDMSC-2404 Crossmark XML

Received:: 01 Jan 2026
Published Online:: 20 Jun 2026
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-2404
Pages:: 2251–2259

Abstract

A graph geodesic polynomial is an algebraic expression linked with its polynomial that gathers information about geodesics, which means shortest paths in a graph connecting two vertices. Examining these polynomials’ characteristics and behaviors, and how they interact with the underlying network, graph structure is necessary for researching the geodesic polynomials of graphs and their vertices. In this paper, we present geodesic polynomials for fan graphs, merging of two star graphs, hericyclic graphs formed by attaching n edges at one or all vertices of C3, Helm graph and geodesic polynomial at a vertex for star graphs and the extended star graphs.

Keywords

Geodesic polynomial Geodesic polynomial at a vertex Geodesic path Eccentricity Diameter

Subject Classifications

05C1005C3805C78

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