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25 results on '"Scapellato, R."'

1. Finite groups with the same Power graph

Author

Mirzargar, M. and Scapellato, R.

Subjects
Mathematics - Group Theory, 05C69, F.2.2
Abstract

The power graph P(G) of a group G is a graph with vertex set G, where two vertices u and v are adjacent if and only if one is the power of the other. In this paper, we raise and study the following question: For which natural numbers n every two groups of order n with isomorphic power graphs are isomorphic? In particular, we determine prove that all such n are cube-free and are not multiples of 16. Moreover, we show that if two finite groups have isomorphic power graphs and one of them is nilpotent or has a normal Hall subgroup, the same is true with the other one., Comment: 9 pages

Published
2020

8. Finite groups with the same power graph.

Author

Mirzargar, M. and Scapellato, R.

Subjects
FINITE groups, NATURAL numbers, CHARTS, diagrams, etc., NILPOTENT groups, ODD numbers
Abstract

The power graph P(G) of a group G is a graph with vertex set G, where two vertices u and v are adjacent if and only if u ≠ v and u m = v or v m = u for some positive integer m. In this paper, we raise and study the following question: For which natural numbers n every two groups of order n with isomorphic power graphs are isomorphic? In particular, it is proved that all such odd number n are cube-free and also they are not multiples of 16 in general. Moreover, we show that if two finite groups have isomorphic power graphs and one of them is nilpotent, the same is true for the other one. [ABSTRACT FROM AUTHOR]

Published
2022
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13. Betweenness centrality: Extremal values and structural properties

Author

Naimzada, A, Stefani, S, Torriero, A, Grassi, R, Scapellato, R, GRASSI, ROSANNA, STEFANI, SILVANA, Torriero, A., Naimzada, A, Stefani, S, Torriero, A, Grassi, R, Scapellato, R, GRASSI, ROSANNA, STEFANI, SILVANA, and Torriero, A.

Abstract

In this paper we investigate the structural properties of betweenness cen-trality and determine some cases in which betweenness reaches its extremal values. Special attention is paid to Star(G), the set of vertices adjacent to all other vertices in a graph and we prove several results about the betweenness of the elements of this set. We introduce the new concept of total betweenness and relate it to group betweenness. We prove a necessary and sufficient condition for the two measures to coincide. Next we consider cutsets and cutvertices and we find a lower bound for their betweenness; in particular for a cutvertex this lower bound is the cutting number. Finally we apply the previous results to trees, proving an alternative formula for betweenness based on cutvertex properties.

Published
2009

16. A note on orthogonal double covers of complete bipartite graphs by a special class of six caterpillars

Author

El-Shanawany, R.A., Higazy, M., Scapellato, R., and Arumugam, S.

Abstract

AbstractWe construct orthogonal double covers of Kn, nby Pm+1≼*Sn-m, where nand mare integers, 2 ≤ m≤ 10, m≤ nand Pm+1≼*Sn-mis a tree obtained from the path Pm+1with medges and a star Sn-mwith n - medges by identifying an end-vertex of Pm+1with the center of Sn-m.

Published
2010
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19. Imprimitive Representations of SL(2, 2k)

Author

Marusic, D. and Scapellato, R.

Abstract

Imprimitive representations of SL(2, 2k), with PG(1, 2k) as the complete block system of imprimitivity, are characterized via their orbital graphs. A description of all graphs admitting the above imprimitive representations of SL(2, 2k) is also given.Copyright 1993, 1999 Academic Press

Published
1993
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25. Betweenness centrality: Extremal values and structural properties

Author

Anna Torriero, Silvana Stefani, R. Scapellato, Rosanna Grassi, Naimzada, A, Stefani, S, Torriero, A, Grassi, R, and Scapellato, R

Subjects
graph, betweenness centrality, geodesic, cutvertex, cutset, graphs, trees, betweenness, Settore SECS-S/06 - METODI MATEMATICI DELL'ECONOMIA E DELLE SCIENZE ATTUARIALI E FINANZIARIE, Combinatorics, Betweenness centrality, Graph, betweenness centrality, geodesic, cutvertex, cutset, SECS-S/06 - METODI MATEMATICI DELL'ECONOMIA E DELLE SCIENZE ATTUARIALI E FINANZIARIE, Mathematics
Abstract

In this paper we investigate the structural properties of betweenness cen-trality and determine some cases in which betweenness reaches its extremal values. Special attention is paid to Star(G), the set of vertices adjacent to all other vertices in a graph and we prove several results about the betweenness of the elements of this set. We introduce the new concept of total betweenness and relate it to group betweenness. We prove a necessary and sufficient condition for the two measures to coincide. Next we consider cutsets and cutvertices and we find a lower bound for their betweenness; in particular for a cutvertex this lower bound is the cutting number. Finally we apply the previous results to trees, proving an alternative formula for betweenness based on cutvertex properties.

Published
2009

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