<abstract xmlns="http://www.w3.org/1999/xhtml"><p>Three main tools to study graphs mathematically are to make use of the vertex degrees, distances and matrices. The classical graph energy was defined by means of the adjacency matrix in 1978 by Gutman and has a large number of applications in chemistry, physics and related areas. As a result of its importance and numerous applications, several modifications of the notion of energy have been introduced since then. Most of them are defined by means of graph matrices constructed by vertex degrees. In this paper we define another type of energy called <italic>q</italic>-distance energy by means of distances and matrices. We study some fundamental properties and also establish some upper and lower bounds for this new energy type.</p></abstract>

Three main tools to study graphs mathematically are to make use of the vertex degrees, distances and matrices. The classical graph energy was defined by means of the adjacency matrix in 1978 by Gutman and has a large number of applications in chemistry, physics and related areas. As a result of its importance and numerous applications, several modifications of the notion of energy have been introduced since then. Most of them are defined by means of graph matrices constructed by vertex degrees. In this paper we define another type of energy called q-distance energy by means of distances and matrices. We study some fundamental properties and also establish some upper and lower bounds for this new energy type.

On Solutions of Fractional order Telegraph Partial Differential Equation by Crank-Nicholson Finite Difference Method

Faculty of Arts and Science, Department of Mathematics

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

Three main tools to study graphs mathematically are to make use of the vertex degrees, distances and matrices. The classical graph energy was defined by means...

On Solutions of Fractional order Telegraph Partial Differential Equation by Crank-Nicholson Finite Difference Method

Published Online: Aug 10, 2020

Page range: 85 - 98

Received: Apr 04, 2019

Accepted: Apr 17, 2019

DOI: https://doi.org/10.2478/amns.2020.2.00017

Keywords
-distance matrix, -distance eigenvalues, -distance energy, join of graphs, union of graphs

© 2020 M. R. Rajesh Kanna et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

On Solutions of Fractional order Telegraph Partial Differential Equation by Crank-Nicholson Finite Difference Method

Published Online: Aug 10, 2020

Page range: 85 - 98

Received: Apr 04, 2019

Accepted: Apr 17, 2019

DOI: https://doi.org/10.2478/amns.2020.2.00017

Keywords-distance matrix, -distance eigenvalues, -distance energy, join of graphs, union of graphs

© 2020 M. R. Rajesh Kanna et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
-distance matrix, -distance eigenvalues, -distance energy, join of graphs, union of graphs