In order to store a graph or digraph in a computer, we need something other than the diagram or the formal definition. This something is the adjacency matrix, a matrix of O’s and l’s. The l’s correspond to the arcs of the digraph. Certain matrix operations will be seen to correspond to digraph concepts.

Graphs and Matrices

This paper describes the bibliometric characteristics of 1,319 articles published in the journal MATCH Communications in Mathematical and in Computer Chemistry, in the period 1995-2014. These articles have been analysed using data from the Web of Science Core Collection and demonstrate the contribution of the journal not only to mathematical and computer chemistry but also to science more generally.

A Bibliometric Profile of MATCH Communications in Mathematical and in Computer Chemistry

In Discrete Math. 184 (1998) 267, the authors extended the splitting operation of graphs to binary matroids. In this paper, we characterize the set of bases of a splitting matroid and give some of its applications.

Determination of the bases of a splitting matroid

In this paper, we introduce the notion of generalized split- ting operation for binary matroids as an extension of the corresponding operation for graphs. The circuits and the bases of the new matroid are characterized. Under the reverse operation, we determine those binary matroids, each of which yields a given matroid by applying the splitting operation on them.

http://icm2006.org/v_f/AbsDef/Shorts/abs_1218.pdf

Generalized Splitting Operation for Binary Matroids and its Applications

We establish upper and lower bounds for the influence of a set of nodes in certain types of contagion models. We derive two sets of bounds, the first designed for linear threshold models, and the second more broadly applicable to a general class of triggering models, which subsumes the popular independent cascade models, as well. We quantify the gap between our upper and lower bounds in the case of the linear threshold model and illustrate the gains of our upper bounds for independent cascade models in relation to existing results. Importantly, our lower bounds are monotonic and submodular, implying that a greedy algorithm for influence maximization is guaranteed to produce a maximizer within a (1 - 1/e)-factor of the truth. Although the problem of exact influence computation is NP-hard in general, our bounds may be evaluated efficiently. This leads to an attractive, highly scalable algorithm for influence maximization with rigorous theoretical guarantees.

/pdf/computing-and-maximizing-influence-in-linear-threshold-and-7rlw7erctp.pdf

Computing and maximizing influence in linear threshold and triggering models

Splitting in a binary matroid

Excluded-Minors For The Class Of Graphic Splitting Matroids.

In this paper, we obtain explicit formulae for the total number of paths of lengths 3 and 4 in a simple graph G. We also determine some formulae for the number of paths of lengths 3 and 4 each of which starts from an specific vertex vi and for the number of vi-vj paths of lengths 3 and 4 in a simple graph G, in terms of the adjacency matrix and with the helps of combinatorics. Keywords: Adjacency Matrix, Cycle, Graph Theory, Path, Subgraph, Walk .

/pdf/on-the-number-of-paths-of-lengths-3-and-4-in-a-graph-4uzrphgyto.pdf

M. M. Shikare

Papers

Splitting in a binary matroid

Determination of the bases of a splitting matroid

Excluded-Minors For The Class Of Graphic Splitting Matroids.

On the number of paths of lengths 3 and 4 in a graph

Generalized Splitting Operation for Binary Matroids and its Applications