RICHNESS OF A VERTEX IN A GRAPH

Print ISSN: 0972-7752 | Online ISSN: 2582-0850 | Total Downloads : 150

Volume : 18 , Issue : 2
DOI: 10.56827/SEAJMMS.2022.1802.14
Author :
R. Rajendra (Department of Mathematics, Field Marshal K M Cariappa College, Madikeri - 571201, Karnataka, INDIA)
P. Siva Kota Reddy (Department of Mathematics, Sri Jayachamarajendra College of Engineering, JSS Science and Technology University, Mysuru - 570006, INDIA)
K. B. Mahesh (Dr. P. Dayananda Pai-P. Sathisha Pai Govt. First Grade College, Mangalore, Carstreet, Mangaluru - 575001, INDIA)
C. N. Harshavardhana (Department of Mathematics, Government First Grade College for Women, Holenarasipur - 573211, INDIA)

Abstract

The stress of a vertex in a graph is the number of geodesics passing through it. The status of a vertex $v$ in a graph is the sum of the distances from $v$ to all other vertices. We define the richness of a vertex $v$ in a graph as the status of $v$ minus the stress of $v$. The total richness of a graph is the sum of richness of all the vertices in that graph. We made some observations, compute richness of vertices in some standard graphs and obtain some interesting results.

Keywords and Phrases

Geodesic, stress of a vertex, status of a vertex.

A.M.S. subject classification

05C12.

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