# IJPAM: Volume 103, No. 1 (2015)

THE FORCING EDGE-TO-VERTEX GEODETIC
NUMBER OF A GRAPH

S. Sujitha , J. John , A. Vijayan  Department of Mathematics
Holy Cross College (Autonomous)
Nagercoil, 629004, INDIA Department of Mathematics
Government College of Engineering
Tirunelveli, 627007, INDIA Department of Mathematics
N.M. Christian College
Marthandam, 629165, INDIA

Abstract. For a connected graph , a set is called an edge-to-vertex geodetic set of if every vertex of is either incident with an edge of or lies on a geodesic joining a pair of edges of . The minimum cardinality of an edge-to-vertex geodetic set of is . Any edge-to-vertex geodetic set of cardinality is called an edge-to-vertex geodetic basis of . A subset is called a forcing subset for if is the unique minimum edge-to-vertex geodetic set containing . A forcing subset for of minimum cardinality is a minimum forcing subset of . The forcing edge-to-vertex geodetic number of , denoted by , is the cardinality of a minimum forcing subset of . The forcing edge-to-vertex geodetic number of , denoted by , is , where the minimum is taken over all minimum edge-to-vertex geodetic sets in . Some general properties satisfied by the concept forcing edge-to-vertex geodetic number is studied. The forcing edge-to-vertex geodetic number of certain classes of graphs are determined. It is shown that for every pair of integers with , there exists a connected graph such that and .

Received: April 21, 2015

AMS Subject Classification: 05C12

Key Words and Phrases: edge-to-vertex geodetic number, forcing edge-to-vertex geodetic number

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DOI: 10.12732/ijpam.v103i1.9 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 103
Issue: 1
Pages: 109 - 121 This work is licensed under the Creative Commons Attribution International License (CC BY).