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Your search keyword '"Julian A. Allagan"' showing total 18 results
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18 results on '"Julian A. Allagan"'

2. Chromatic Polynomials Of Some (m,l)-Hyperwheels

Author

Julian A. Allagan

Subjects
chromatic polynomial, hyperfan, hyperwheel, Stirling numbers, Electronic computers. Computer science, QA75.5-76.95
Abstract

In this paper, using a standard method of computing the chromatic polynomial of hypergraphs, we introduce a new reduction theorem which allows us to find explicit formulae for the chromatic polynomials of some (complete) non-uniform $(m,l)-$hyperwheels and non-uniform $(m,l)-$hyperfans. These hypergraphs, constructed through a ``join" graph operation, are some generalizations of the well-known wheel and fan graphs, respectively. Further, we revisit some results concerning these graphs and present their chromatic polynomials in a standard form that involves the Stirling numbers of the second kind.

Published
2014

3. Tutte Polynomial of Multi-Bridge Graphs

Author

Julian A. Allagan

Subjects
Tutte polynomial, multi-bridge graph, 2-tree, fan, wheel, Electronic computers. Computer science, QA75.5-76.95
Abstract

In this paper, using a well-known recursion for computing the Tutte polynomial of any graph, we found explicit formulae for the Tutte polynomials of any multi-bridge graph and some $2-$tree graphs. Further, several recursive formulae for other graphs such as the fan and the wheel graphs are also discussed.

Published
2013

4. A generalization of the chromatic polynomial of a cycle

Author

Julian A. Allagan

Subjects
Electronic computers. Computer science, QA75.5-76.95
Abstract

We prove that if an edge of a cycle on vertices is extended by adding vertices, then the the chromatic polynomial of such generalized cycle is: $$P(H_k,\lambda)=(\lambda-1)^n\sum_{i=0}^k \lambda^i+(-1)^n(\lambda-1).$$

Published
2005

16. Chromatic Spectrum of $K_s$-WORM Colorings of $K_n$

Author

Julian A.D. Allagan and Kenneth L. Jones

Subjects
mixed hypergraph coloring, chromatic spectrum, lcsh:Electronic computers. Computer science, stirling numbers, catalan numbers, lcsh:QA75.5-76.95
Abstract

An {\it $H$-WORM} coloring of a simple graph $G$ is the coloring of the vertices of $G$ such that no copy of $H\subseteq G$ is monochrome or rainbow. In a recently published article by one of the authors \cite{All1}, it was claimed that the number of $r$-partitions in a $K_s$-WORM coloring of $K_n$ is $ \zeta_r=\stirr{n}{r}$, where $\stirr{n}{r}$ denotes the Stirling number of the second kind, for all $3\le r\le s < n$. We found that $ \displaystyle \zeta_r = \stirr{n}{r}$ if and only if ${\lceil \frac{n+3}{2} \rceil}

Published
2020

18. Tutte polynomial of some multigraphs

Author

Julian A. Allagan and Eunice Mphako-Banda

Subjects
Discrete mathematics, Combinatorics, Mathematics (miscellaneous), Explicit formulae, Computation, Multigraph, Tutte 12-cage, Tutte polynomial, Tutte matrix, Chromatic polynomial, Tutte theorem, Mathematics
Abstract

Using two related parameters, ζ and γ, we extend the recursion for com- puting the Tutte polynomial of any graph to the computation of the Tutte polynomial of any multigraph. With this recursion, we found explicit formulae for several fami- lies of multigraphs. In particular, the Tutte polynomials of some cyclic multigraphs, 2−tree multigraphs, and any l−bridge multigraph.

Published
2015
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