Complementary Distance Spectra and Complementary Distance Energy of Linegraphs of Regular Graphs  

Oleh:

Ramane, H. S. ; Nandeesh, K. C.

Jenis: Article from Journal - ilmiah nasional - terakreditasi DIKTI
Dalam koleksi: Journal of the Indonesian Mathematical Society vol. 22 no. 1 (Apr. 2016), page 27-35.
Topik: Complementary distance eigenvalues; adjacency eigenvalues; line graphs; complementary distance energy; Nilai-nilai eigen complementary distance; Nilai-nilai eigen ketetanggaan; graf-graf garis; energi complementary distance.
Fulltext: 205-622-1-PB.pdf (305.77KB)

Isi artikel

The complementary distance (CD) matrix of a graph G is dened as CD(G) = [c ij ], where c ij = 1 + D d ij if i 6 = j and c = 0, otherwise, where D is the diameter of G and d ij ij is the distance between the vertices v in G. The CD-energy of G is dened as the sum of the absolute values of the eigenvalues of CD-matrix. Two graphs are said to be CD-equienergetic if they have same CD-energy. In this paper we show that the complement of the line graph of certain regular graphs has exactly one positive CD-eigenvalue. Further we obtain the CD-energy of line graphs of certain regular graphs and thus constructs pairs of CD-equienergetic graphs of same order and having dierent CD-eigenvalues.

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