<abstract xmlns="http://www.w3.org/1999/xhtml">The degree distance <italic>DD</italic>(<italic>G</italic>) of a connected graph <italic>G</italic> was invented by Dobrynin and Kochetova in 1994. Recently, one of the present authors introduced the concept of <italic>k</italic>-center Steiner degree distance defined as 
<disp-formula><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_auom-2019-0020_eq_001.png"></graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>SDD</mi><mi>k</mi></msub><mo>(</mo><mi>G</mi><mo>)</mo><mo>=</mo><mstyle><munder><mo>∑</mo><mrow><mtable><mtr><mtd><mrow><mi>S</mi><mo>⊆</mo><mi>V</mi><mo>(</mo><mi>G</mi><mo>)</mo></mrow></mtd></mtr><mtr><mtd><mrow><mrow><mo>|</mo><mi>S</mi><mo>|</mo></mrow><mo>=</mo><mi>k</mi></mrow></mtd></mtr></mtable></mrow></munder><mrow><mrow><mo>[</mo><mrow><mstyle><munder><mo>∑</mo><mrow><mi>v</mi><mo>∈</mo><mi>S</mi></mrow></munder><mrow><msub><mrow><mi>deg</mi><mo>⁡</mo></mrow><mi>G</mi></msub><mo>(</mo><mi>v</mi><mo>)</mo></mrow></mstyle></mrow><mo>]</mo></mrow><msub><mi>d</mi><mi>G</mi></msub><mo>(</mo><mi>S</mi><mo>)</mo><mo>,</mo></mrow></mstyle></mrow></math><tex-math>SDD_k (G) = \sum\limits_{\mathop {S \subseteq V(G)}\limits_{\left| S \right| = k} } {\left[ {\sum\limits_{v \in S} {{\it deg} _G (v)} } \right]d_G (S),} </tex-math></alternatives></disp-formula>
where <italic>dG</italic>(<italic>S</italic>) is the Steiner <italic>k</italic>-distance of <italic>S</italic> and <italic>degG</italic>(<italic>v</italic>) is the degree of the vertex <italic>v</italic> in <italic>G</italic>. In this paper, we investigate the Steiner degree distance of complete and Cartesian product graphs.</abstract>

The degree distance DD(G) of a connected graph G was invented by Dobrynin and Kochetova in 1994. Recently, one of the present authors introduced the concept of k-center Steiner degree distance defined as 
SDDk(G)=∑S⊆V(G)|S|=k[∑v∈Sdeg⁡G(v)]dG(S),SDD_k (G) = \sum\limits_{\mathop {S \subseteq V(G)}\limits_{\left| S \right| = k} } {\left[ {\sum\limits_{v \in S} {{\it deg} _G (v)} } \right]d_G (S),} 
where dG(S) is the Steiner k-distance of S and degG(v) is the degree of the vertex v in G. In this paper, we investigate the Steiner degree distance of complete and Cartesian product graphs.

Steiner Degree Distance of Two Graph Products

Center for Mathematics and Interdisciplinary Sciences of Qinghai Province

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Steiner Degree Distance of Two Graph Products"}

The degree distance DD(G) of a connected graph G was invented by Dobrynin and Kochetova in 1994. Recently, one of the present authors introduced the concept of...

Steiner Degree Distance of Two Graph Products

Published Online: Sep 26, 2019

Page range: 83 - 99

Received: Apr 10, 2018

Accepted: Jul 30, 2018

DOI: https://doi.org/10.2478/auom-2019-0020

Keywords
Steiner degree distance, Degree distance, Complete product, Cartesian product

© 2019 Yaping Mao et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Steiner Degree Distance of Two Graph Products

Published Online: Sep 26, 2019

Page range: 83 - 99

Received: Apr 10, 2018

Accepted: Jul 30, 2018

DOI: https://doi.org/10.2478/auom-2019-0020

KeywordsSteiner degree distance, Degree distance, Complete product, Cartesian product

© 2019 Yaping Mao et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Steiner degree distance, Degree distance, Complete product, Cartesian product