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Open Journal of Discrete Mathematics (OJDM) is an openly accessible journal published quarterly. The goal of this journal is to provide a platform for scientists and academicians all over the world to promote,share,and discuss various new issues and developments in different areas of discrete mathematics. All manuscri…
Imelda Elohor Agbedo, Ophokpokpo Matthew Salami, Ojiyovwi Rhoda Osanakpa, Oluranran Clinton Kayoh, Ifeanyi Jeff Ugbene
Let X n = { 1 , 2 , ⋯ , n } and let T n denote the full transformation semigroup of all n n maps α : X n → X n . Each α ∈ T n induces a functional digraph Γ α whose vertex set is X n and whose arc set is { ( x , α ( x ) ) : x ∈ X n } . Because every vertex ha…
Wensheng Li, Zhongsheng Huang, Zhifang Feng
A double Roman dominating function (DRDF) f on a given graph G is a mapping from V ( G ) to {0, 1, 2, 3} in such a way that a vertex v for which f ( v ) = 0 has at least a neighbor labeled 3 or two neighbors both labeled 2 and a vertex v for which f ( v ) = 1…
Julian Allagan, Gabrielle Morgan, Shawn Langley
We introduce the bichromatic triangle polynomial P G Δ ( k ) , a chromatic invariant that counts vertex colorings of a graph in which every designated triangular face uses exactly two colors. This polynomial refines classical chromatic counting by imposing lo…
Rao Li
Let G = ( V , E ) be a graph. The first Zagreb index of a graph G is defined as ∑ u ∈ V d G 2 ( u ) , where d G ( u ) is the degree of vertex u in G . In this paper, we obtain two lower bounds involving the independence number for the first Zagreb index of a…
Seonghwan Yang
Let n ≥ 10 be an even integer. It is proved that there exists a prime number p and a composite number c such that n = p + c . The proof is constructed using elementary number theory, incorporating inductive reasoning, deterministic candidate filtering, and co…
Rita Vincenti
This note investigates the hyperplane sections of a ruled variety V 2 2 r − 1 embedded in P G ( 2 r , q ) , which yield caps associated with specific arcs in P G ( 2 , q ) . We construct a partition of the affine points of V 2 2 r − 1 into caps, corresponding…
Muhammad Mansur Zubairu, Zulyadaini D. Lawan
In this paper, we consider the monoid Fix O C T ( [ n ] , D ) of all order-preserving full contraction mappings that fix a subset say D of a finite n -element chain { 1 , 2 , ⋯ , n } . We characterize regularity, Green’s relations, and starred Green’s relatio…
Paul A. Burchett
In this paper, we consider chessboard graphs in higher dimensions and the number of edges of their corresponding graphs. First, we solve for the number of edges for some of the chessboard graphs of 3 dimensions. Then, we obtain results for the number of edges…
Qinglin Jia, Wenwei Zhao, Zhengyuan Jiang, Yongqiang Zhao
In a graph G = ( V , E ) , two disjoint sets V 1 , V 2 ⊆ V are said to form a coalition, if neither V 1 nor V 2 is a dominating set of G , but V 1 ∪ V 2 is a dominating set of G . The sets V 1 and V 2 forming a coalition are said to be coalition partners. A c…
Robinson Santrin Sabibha, Kruz Jeya Daisy, Pon Jeyanthi, Maged Zakaria Youssef, 1 1
In 2012, Ponraj et al . defined a concept of k-product cordial labeling as follows: Let f be a map from V ( G ) to { 0,1, ⋯ , k − 1 } where k is an integer, 1 ≤ k ≤ | V ( G ) | . For each edge u v assign the label f ( u ) f ( v ) ( mod k ) . f is called a k-p…
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Open Journal of Discrete Mathematics (OJDM) is an openly accessible journal published quarterly. The goal of this journal is to provide a platform for scientists and academicians all over the world to promote,share,and discuss various new issues and developments in different areas of discrete mathematics. All manuscri… All articles are open access under a CC BY 4.0 licence, with authors retaining copyright.
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