ON SPECTRA OF TERMINAL D-DISTANCE MATRIX OF SOME CLASS OF GRAPHS
P. R. HAMPIHOLI
Department of Mathematics, KLS Gogte Institute of Technology, Belagavi, Karnataka, India.
ANJANA S. JOSHI
*
Department of Mathematics, KLS Gogte Institute of Technology, Belagavi, Karnataka, India.
P. V. ADHYAPAK
Department of Mathematics, KLS Gogte Institute of Technology, Belagavi, Karnataka, India.
S. R. KABBUR
Department of Mathematics, KLS Gogte Institute of Technology, Belagavi, Karnataka, India.
*Author to whom correspondence should be addressed.
Abstract
In this paper we consider simple graphs, all the vertices with degree one are known as pendent vertices or terminal vertices of a graph. For two terminals vertices of a graph G D-distance is addition of the distance between and the sum of degrees of all the vertices of path , including degrees of . This paper consists of definition of terminal D-distance matrix and computation of terminal D-distance energy of few class of graphs. Bounds on Terminal-D-distance energy are also established.
Keywords: D-distance, spectra, terminal vertex, terminal matrix, energy, bounds
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Randic M, Zupan J. Highly compact 2D graphical representation of DNA sequence, SARQSAR, Environ. Res. 2004;15:191-205.Randic M, Zupan J, Vikic-Topic D. On representation of properties by star like graphs. J. Mol. Graphics and Modelling. 2007;26:290-305.
Indulal G, Gutman I, Vijaykumar A. On the distance energy of graphs. MATCH commun. Math. Comput. Chem. 2008;60:461–472.
Hampiholi PR, Anjana S Joshi, Vinaya V Deshpande. On minimum hub D-distance Spectra of some graphs. International Journal of Mathematics Trends and Technology. 2020;66(12):44-54.
Prabhakar R. Hampiholi, Anjana S. Joshi, Jotiba P. Kitturkar. On spectra of D-eccentricity matrix of some graphs. int. J. Math. And Appl. 2020;8(4):59–68.
Jog S, Gurjar J. Degree product distance energy of some graphs. Asian Journal of Mathematics and Computer Research. 2018;24(1):42-49.
Durgi BS, Hampiholi PR, Mekkalike SM. Distance spectra and distance energy of some cluster graphs. Mathematica Aeterna. 2014;4(8):817–825.
Ramane HS, Patil JB, Revenkar DS. terminal distance energy of graph. International Journal of Graph Theory. 2013;3:82-87.
Reddy Babu D, Varma PLN. D-distance in graphs. Golden Research Thoughts. 2013;2:53–58.
Hovart B. On the calculation of the terminal polynomial of a star like graph. Croat. Chem. Acta. 2009;82:679-684.
Hovart B, Pisanski T, Ranic. Terminal polynomials and star like graphs. MATCH Commun. Math. Compu. Chem. 2008;60:493-512.