On Complementary Distance Signless Laplacian Spectral Radius and Energy of Graphs

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RAMANE HARISHCHANDRA S.; Gudodagi Gouramma A.; Manjalapur Vinayak V.; Alhevaz Abdollah

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Journal: Iranian Journal of Mathematical Sciences and Informatics Year:2019 | Volume:14 | Issue:2 Page(s): 105-125

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Title

On Complementary Distance Signless Laplacian Spectral Radius and Energy of Graphs

Author(s)

RAMANE HARISHCHANDRA S. | Gudodagi Gouramma A. | Manjalapur Vinayak V. | Alhevaz Abdollah | Issue Writer Certificate

Keywords

Complementary distance signless Laplacian matrix (energy)

diameter

complementary transmission regular graph

Abstract

Let D be the diameter and dG(vi, vj ) be the distance between the vertices vi and vj of a connected graph G. The complementary distance matrix of a graph G is CD(G) = [cdij ] in which cdij = 1 +D − dG(vi, vj ) if i 6= j and cdij = 0 if i = j. The complementary transmission CTG(v) of a vertex v is defined as CTG(v) = Pu2V (G)[1+D− dG(u, v)]. Let CT(G) = diag[CTG(v1), CTG(v2), . . ., CTG(vn)]. The complementary distance signless Laplacian matrix of G is CDL+(G) = CT(G) + CD(G). In this paper, we obtain the bounds for the largest eigenvalue of CDL+(G). Further we determine Nordhaus-Gaddum type results for the largest eigenvalue. We also establish some bounds for the complementary distance signless Laplacian energy.

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APA: Copy

RAMANE, HARISHCHANDRA S., Gudodagi, Gouramma A., Manjalapur, Vinayak V., & Alhevaz, Abdollah. (2019). On Complementary Distance Signless Laplacian Spectral Radius and Energy of Graphs. IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI), 14(2), 105-125. SID. https://sid.ir/paper/310499/en

Vancouver: Copy

RAMANE HARISHCHANDRA S., Gudodagi Gouramma A., Manjalapur Vinayak V., Alhevaz Abdollah. On Complementary Distance Signless Laplacian Spectral Radius and Energy of Graphs. IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI)[Internet]. 2019;14(2):105-125. Available from: https://sid.ir/paper/310499/en

IEEE: Copy

HARISHCHANDRA S. RAMANE, Gouramma A. Gudodagi, Vinayak V. Manjalapur, and Abdollah Alhevaz, “On Complementary Distance Signless Laplacian Spectral Radius and Energy of Graphs,” IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI), vol. 14, no. 2, pp. 105–125, 2019, [Online]. Available: https://sid.ir/paper/310499/en

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