Open AccessOn the Vertex Multiplication Graphs
Author(s) -
M. Saravanan,
K. Kathiresan
Publication year - 2019
Publication title -
international journal of engineering and advanced technology
Language(s) - English
Resource type - Journals
ISSN - 2249-8958
DOI - 10.35940/ijeat.a1209.1291s419
Subject(s) - combinatorics , mathematics , circulant graph , vertex (graph theory) , wheel graph , windmill graph , symmetric graph , discrete mathematics , regular graph , neighbourhood (mathematics) , graph , line graph , graph power , voltage graph , mathematical analysis
For any graph , with vertex set { } and a p-tuble of positive integers , the vertex multiplication graph is defined as the graph with vertex set consists of copies of each , where the copies of and are adjacent in if and only if the corresponding vertices and are adjacent in G . In this paper, we prove that the spectrum of is same as that of spectrum of its quotient graph with additional zero eigenvalues with multiplicity , where . Also we prove that the determinant of is minimum for and maximum for . Also we find distance- i spectrum of thorn graphs, , when G is connected - regular graph with diameter 2.