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

**THE FORCING EDGE-TO-VERTEX GEODETIC**

NUMBER OF A GRAPH

NUMBER OF A GRAPH

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**

International Journal of Pure and Applied Mathematics

**How to cite this paper?****Source:****ISSN printed version:**1311-8080

**ISSN on-line version:**1314-3395

**Year:**2015

**Volume:**103

**Issue:**1

**Pages:**109 - 121

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**This work is licensed under the Creative Commons Attribution International License (CC BY).**