2,327 research outputs found
Outer Independent Double Italian Domination of Some Graph Products
An outer independent double Italian dominating function on a graph is a function for which each vertex with then and vertices assigned under are independent. The outer independent double Italian domination number is the minimum weight of an outer independent double Italian dominating function of graph . In this work, we present some contributions to the study of outer independent double Italian domination of three graph products. We characterize the Cartesian product, lexicographic product and direct product of custom graphs in terms of this parameter. We also provide the best possible upper and lower bounds for these three products for arbitrary graphs
Outer independent square free detour number of a graph
For a connected graph , a set  of vertices is called an outer independent square free detour set if  is a square free detour set of  such that either  or is an independent set. The minimum cardinality of an outer independent square free detour set of  is called an outer independent square free detour number of  and is denoted by  We determine the outer independent square free detour number of some graphs. We characterize the graph which realizes the result that for any pair of integers  and  with there exists a connected graph  of order  with square free detour number and outer independent square free detour number
Theoretical Computer Science and Discrete Mathematics
This book includes 15 articles published in the Special Issue "Theoretical Computer Science and Discrete Mathematics" of Symmetry (ISSN 2073-8994). This Special Issue is devoted to original and significant contributions to theoretical computer science and discrete mathematics. The aim was to bring together research papers linking different areas of discrete mathematics and theoretical computer science, as well as applications of discrete mathematics to other areas of science and technology. The Special Issue covers topics in discrete mathematics including (but not limited to) graph theory, cryptography, numerical semigroups, discrete optimization, algorithms, and complexity
A constructive characterization of vertex cover Roman trees
A Roman dominating function on a graph G = (V (G), E (G)) is a function f : V (G) -> {0, 1, 2} satisfying the condition that every vertex u for which f (u) = 0 is adjacent to at least one vertex v for which f (v) = 2. The Roman dominating function f is an outer-independent Roman dominating function on G if the set of vertices labeled with zero under f is an independent set. The outer-independent Roman domination number gamma(oiR) (G) is the minimum weight w(f ) = Sigma(v is an element of V), ((G)) f(v) of any outer-independent Roman dominating function f of G. A vertex cover of a graph G is a set of vertices that covers all the edges of G. The minimum cardinality of a vertex cover is denoted by alpha(G). A graph G is a vertex cover Roman graph if gamma(oiR) (G) = 2 alpha(G). A constructive characterization of the vertex cover Roman trees is given in this article
Spartan Daily, May 11, 1967
Volume 54, Issue 118https://scholarworks.sjsu.edu/spartandaily/4984/thumbnail.jp
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