scholarly journals Strongly distance-balanced graphs and graph products

2009 ◽  
Vol 30 (5) ◽  
pp. 1048-1053 ◽  
Author(s):  
Kannan Balakrishnan ◽  
Manoj Changat ◽  
Iztok Peterin ◽  
Simon Špacapan ◽  
Primož Šparl ◽  
...  
Keyword(s):  
Graph Products ◽  
Balanced Graphs

scholarly journals Further Remarks on n-Distance-Balanced Graphs

2019 ◽  
Vol 25 (1) ◽  
pp. 44-61
Author(s):  
Morteza Faghani ◽  
Ehsan Pourhadi
Keyword(s):  
Bipartite Graphs ◽  
Graph Products ◽  
Szeged Index ◽  
Strong Property ◽  
Balanced Graphs

Throughout this paper, we present a new strong property of graph so-called nicely n-distance-balanced which is notably stronger than the concept of n-distance-balanced recently given by the authors. We also initially introduce a newgraph invariant which modies Szeged index and is suitable to study n-distance-balanced graphs. Looking for the graphs extremal with respect to the modiedSzeged index it turns out the n-distance-balanced graphs with odd integer n arethe only bipartite graphs which can maximize the modied Szeged index and thisalso disproves a conjecture proposed by Khalifeh et al. [Khalifeh M.H.,Youse-Azari H., Ashra A.R., Wagner S.G.: Some new results on distance-based graphinvariants, European J. Combin. 30 (2009) 1149-1163]. Furthermore, we gathersome facts concerning with the nicely n-distance-balanced graphs generated by somewell-known graph products. To enlighten the reader some examples are provided.Moreover, a conjecture and a problem are presented within the results of this article.

On two conjectures on b-coloring of graph products

2017 ◽  
Vol 54 (1) ◽  
pp. 141-149
Author(s):  
S. Francis Raj ◽  
T. Kavaskar
Keyword(s):  
Graph Products

Tenacity of complete graph products and grids

Networks ◽  
1999 ◽  
Vol 34 (3) ◽  
pp. 192-196 ◽  
Author(s):  
S. A. Choudum ◽  
N. Priya
Keyword(s):  
Complete Graph ◽  
Graph Products

THE DIAMETER VARIABILITY OF THE CARTESIAN PRODUCT OF GRAPHS

2014 ◽  
Vol 06 (01) ◽  
pp. 1450001 ◽  
Author(s):  
M. R. CHITHRA ◽  
A. VIJAYAKUMAR
Keyword(s):  
Interconnection Networks ◽  
Cartesian Product ◽  
Graph Products ◽  
Single Edge ◽  
Cartesian Product Of Graphs ◽  
Product Of Graphs

The diameter of a graph can be affected by the addition or deletion of edges. In this paper, we examine the Cartesian product of graphs whose diameter increases (decreases) by the deletion (addition) of a single edge. The problems of minimality and maximality of the Cartesian product of graphs with respect to its diameter are also solved. These problems are motivated by the fact that most of the interconnection networks are graph products and a good network must be hard to disrupt and the transmissions must remain connected even if some vertices or edges fail.

Graph products of groups and group spaces

1995 ◽  
Vol 53 (1-2) ◽  
pp. 131-147 ◽  
Author(s):  
Jochen Pfalzgraf
Keyword(s):  
Graph Products ◽  
Products Of Groups

scholarly journals Graph diffusion distance: Properties and efficient computation

PLoS ONE ◽  
2021 ◽  
Vol 16 (4) ◽  
pp. e0249624
Author(s):  
C. B. Scott ◽  
Eric Mjolsness
Keyword(s):  
Distance Measure ◽  
Fixed Time ◽  
Graph Laplacian ◽  
Upper Bounds ◽  
Distance Measures ◽  
Distance Metrics ◽  
Graph Products ◽  
Efficient Computation ◽  
New Family ◽  
Sparsity Constraints

We define a new family of similarity and distance measures on graphs, and explore their theoretical properties in comparison to conventional distance metrics. These measures are defined by the solution(s) to an optimization problem which attempts find a map minimizing the discrepancy between two graph Laplacian exponential matrices, under norm-preserving and sparsity constraints. Variants of the distance metric are introduced to consider such optimized maps under sparsity constraints as well as fixed time-scaling between the two Laplacians. The objective function of this optimization is multimodal and has discontinuous slope, and is hence difficult for univariate optimizers to solve. We demonstrate a novel procedure for efficiently calculating these optima for two of our distance measure variants. We present numerical experiments demonstrating that (a) upper bounds of our distance metrics can be used to distinguish between lineages of related graphs; (b) our procedure is faster at finding the required optima, by as much as a factor of 103; and (c) the upper bounds satisfy the triangle inequality exactly under some assumptions and approximately under others. We also derive an upper bound for the distance between two graph products, in terms of the distance between the two pairs of factors. Additionally, we present several possible applications, including the construction of infinite “graph limits” by means of Cauchy sequences of graphs related to one another by our distance measure.

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