3,491 research outputs found
Super edge-magic deficiency of join-product graphs
A graph is called \textit{super edge-magic} if there exists a bijective
function from to such
that and is a
constant for every edge of . Furthermore, the \textit{super
edge-magic deficiency} of a graph is either the minimum nonnegative integer
such that is super edge-magic or if there exists no
such integer.
\emph{Join product} of two graphs is their graph union with additional edges
that connect all vertices of the first graph to each vertex of the second
graph. In this paper, we study the super edge-magic deficiencies of a wheel
minus an edge and join products of a path, a star, and a cycle, respectively,
with isolated vertices.Comment: 11 page
Recent studies on the super edge-magic deficiency of graphs
A graph is called edge-magic if there exists a bijective function
such that is a constant for each . Also,
is said to be super edge-magic if . Furthermore, the
super edge-magic deficiency of a graph is defined
to be either the smallest nonnegative integer with the property that is super edge-magic or if there exists no such integer
. In this paper, we introduce the parameter as the minimum
size of a graph of order for which all graphs of order and size at
least have , and provide
lower and upper bounds for . Imran, Baig, and
Fe\u{n}ov\u{c}\'{i}kov\'{a} established that for integers with , , where is the
cartesian product of the cycle of order and the complete graph
of order . We improve this bound by showing that when is even. Enomoto,
Llad\'{o}, Nakamigawa, and Ringel posed the conjecture that every nontrivial
tree is super edge-magic. We propose a new approach to attak this conjecture.
This approach may also help to resolve another labeling conjecture on trees by
Graham and Sloane
Super Edge-magic Labeling of Graphs: Deficiency and Maximality
A graph G of order p and size q is called super edge-magic if there exists a bijective function f from V(G) U E(G) to {1, 2, 3, ..., p+q} such that f(x) + f(xy) + f(y) is a constant for every edge and f(V(G)) = {1, 2, 3, ..., p}. The super edge-magic deficiency of a graph G is either the smallest nonnegative integer n such that G U nK_1 is super edge-magic or +~ if there exists no such integer n. In this paper, we study the super edge-magic deficiency of join product graphs. We found a lower bound of the super edge-magic deficiency of join product of any connected graph with isolated vertices and a better upper bound of the super edge-magic deficiency of join product of super edge-magic graphs with isolated vertices. Also, we provide constructions of some maximal graphs, ie. super edge-magic graphs with maximal number of edges
Magic and antimagic labeling of graphs
"A bijection mapping that assigns natural numbers to vertices and/or edges of a graph is called a labeling. In this thesis, we consider graph labelings that have weights associated with each edge and/or vertex. If all the vertex weights (respectively, edge weights) have the same value then the labeling is called magic. If the weight is different for every vertex (respectively, every edge) then we called the labeling antimagic. In this thesis we introduce some variations of magic and antimagic labelings and discuss their properties and provide corresponding labeling schemes. There are two main parts in this thesis. One main part is on vertex labeling and the other main part is on edge labeling."Doctor of Philosoph
Montana Kaimin, November 8, 1991
Student newspaper of the University of Montana, Missoula.https://scholarworks.umt.edu/studentnewspaper/9460/thumbnail.jp
Spartan Daily, March 19, 1992
Volume 98, Issue 39https://scholarworks.sjsu.edu/spartandaily/8252/thumbnail.jp
Enhancing Students' Combinatorial Thinking for Graceful Coloring Problem: A STEM-Based, Research-Informed Approach in ATM Placement
Combinatorial generalization thinking, a component of higher-order thinking skills, encompasses perception (pattern identification), expressions (pattern illustration), symbolic expressions (pattern formulation), and manipulation (combinatorial results application). Implementing a research-based learning (RBL) model with a Science, Technology, Engineering, and Mathematics (STEM) approach can effectively transform students' learning processes, promoting experiential learning through the integration of STEM elements. This study employs a mixed-method research design, combining quantitative and qualitative methodologies, to evaluate the impact of this RBL-STEM model on students' ability to solve graceful coloring problems, hence developing their combinatorial thinking skills. Two distinct classes, one experimental and one control, were analyzed for statistical homogeneity, normality, and independent t-test comparisons. Results indicated a significant post-test t-score difference between the two groups. Consequently, we conclude that the RBL model with a STEM approach significantly enhances students' combinatorial generalization thinking skills in solving graceful coloring problems. As this research provides empirical evidence of the effectiveness of a STEM-based RBL model, educators, and curriculum developers are encouraged to incorporate this approach into their instructional strategies for enhancing combinatorial thinking skills. Future research should consider various contexts and diverse student populations to further validate and generalize these findings
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