Open AccessOn Tosha-degree of an Edge in a Graph
Author(s) -
R. Rajendra,
P. Siva Kota Reddy
Publication year - 2020
Publication title -
european journal of pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.245
H-Index - 5
ISSN - 1307-5543
DOI - 10.29020/nybg.ejpam.v13i5.3710
Subject(s) - multigraph , mathematics , adjacency matrix , graph energy , line graph , combinatorics , degree matrix , adjacency list , regular graph , multiple edges , graph , discrete mathematics , strength of a graph , degree (music) , complement graph , voltage graph , graph power , physics , acoustics
In an earlier paper, we have introduced the Tosha-degree of an edge in a graph without multiple edges and studied some properties. In this paper, we extend the definition of Tosha-degree of an edge in a graph in which multiple edges are allowed. Also, we introduce the concepts - zero edges in a graph, $T$-line graph of a multigraph, Tosha-adjacency matrix, Tosha-energy, edge-adjacency matrix and edge energy of a graph $G$ and obtain some results.