Communications in Combinatorics and Optimization
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A new measure for transmission irregularity extent of graphs
(Azarbaijan Shahid Madani University, 2025-12-01)The transmission of a vertex ${\varsigma}$ in a connected graph $\mathcal{J}$ is the sum of distances between ${\varsigma}$ and all other vertices of $\mathcal{J}$. A graph $\mathcal{J}$ is called transmission regular if ...
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Set colorings of the Cartesian product of some graph families
(Azarbaijan Shahid Madani University, 2025-12-01)Neighbor-distinguishing colorings, which are colorings that induce a proper vertex coloring of a graph, have been the focus of different studies in graph theory. One such coloring is the set coloring. For a nontrivial graph ...
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Elliptic Sombor index of chemical graphs
(Azarbaijan Shahid Madani University, 2025-12-01)Let $G$ be a simple graph. The elliptic Sombor index of $G$ is defined as $$ ESO(G) = \sum_{uv} \left(d_{u}+ d_{v} \right)\sqrt{d^{2}_{u}+d^{2}_{v}},$$ where $d_{u}$ denotes the degree of the vertex $u$, and the sum ...
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Complete solutions on local antimagic chromatic number of three families of disconnected graphs
(Azarbaijan Shahid Madani University, 2025-12-01)An edge labeling of a graph $G = (V, E)$ is said to be local antimagic if it is a bijection $f:E \to\{1,\ldots ,|E|\}$ such that for any pair of adjacent vertices $x$ and $y$, $f^+(x)\not= f^+(y)$, where the induced vertex ...
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Triangular type-2 fuzzy goal programming approach for bimatrix games
(Azarbaijan Shahid Madani University, 2025-12-01)This paper addresses a bimatrix game in which the satisfactory degrees of the players are vague. Type-2 fuzzy goal programming technique is used to describe the game. Then, the notion of equilibrium points is introduced ...
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The crossing numbers of join products of $K_4\cup K_1$ with cycles
(Azarbaijan Shahid Madani University, 2025-12-01)The crossing number $\mathrm{cr}(G)$ of a graph $G$ is the minimum number of edge crossings over all drawings of $G$ in the plane. In the paper, we extend known results concerning crossing numbers of join products of two ...
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Global Malmquist productivity index for evaluation of multistage series systems with undesirable and non-discretionary data
(Azarbaijan Shahid Madani University, 2025-12-01)Data Envelopment Analysis measures relative efficiency, in which the performances of the DMUs in a group are compared. In this approach, an efficient unit in one group may be considered inefficient compared to the units ...
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2-semi equivelar maps on the torus and the Klein bottle with few vertices
(Azarbaijan Shahid Madani University, 2025-12-01)The $k$-semi equivelar maps, for $k \geq 2$, are generalizations of maps on the surfaces of Johnson solids to closed surfaces other than the 2-sphere. In the present study, we determine 2-semi equivelar maps of curvature ...
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A hybrid branch-and-bound and interior-point algorithm for stochastic mixed-integer nonlinear second-order cone programming
(Azarbaijan Shahid Madani University, 2025-12-01)One of the chief attractions of stochastic mixed-integer second-order cone programming is its diverse applications, especially in engineering (Alzalg and Alioui, {\em IEEE Access}, 10:3522-3547, 2022). The linear and ...
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Exploring the Precise Edge Irregularity Strength of Generalized Arithmetic and Geometric Staircase Graphs
(Azarbaijan Shahid Madani University, 2025-12-01)In the context of a finite undirected graph $\zeta$, an edge irregular labelling is defined as a labelling of its vertices with some labels in such a way that each edge has a unique weight, which is determined by the sum ...
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Total Roman domination and total domination in unit disk graphs
(Azarbaijan Shahid Madani University, 2025-12-01)Let $G=(V,E)$ be a simple, undirected and connected graph. A Roman dominating function (RDF) on the graph $G$ is a function $f:V\rightarrow\{0,1,2\}$ such that each vertex $v\in V$ with $f(v)=0$ is adjacent to at least one ...
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On $e$-super $(a, d)$-edge antimagic total labeling of total graphs of paths and cycles
(Azarbaijan Shahid Madani University, 2025-12-01)A $(p, q)$-graph $G$ is $(a, d)$-edge antimagic total if there exists a bijection $f$ from $V(G) \cup E(G)$ to $\{1, 2, \dots, p+q\}$ such that for each edge $uv \in E(G)$, the edge weight $\Lambda(uv) = f(u) + f(uv) + ...
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Nonlinear inclusion for thermo-electro-elastic: existence, dependence and optimal control
(Azarbaijan Shahid Madani University, 2025-12-01)The objective of this paper is to examine a model of a thermo-electro-elastic body situated on a semi-insulator foundation. Friction is characterized by Tresca's friction law, and the contact is bilateral. The primary ...
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Leavitt path algebras for order prime Cayley graphs of finite groups
(Azarbaijan Shahid Madani University, 2025-12-01)In this paper, we generalize the concept of Cayley graphs associated to finite groups. The aim of this paper is the characterization of graph theoretic properties of new type of directed graph $\Gamma_P(G;S)$ and algebraic ...
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On connected bipartite $Q$-integral graphs
(Azarbaijan Shahid Madani University, 2025-12-01)A graph $G$ is said to be $H$-free if $G$ does not contain $H$ as an induced subgraph. Let $\mathcal{S}_{n}^2(m)$ be a \textit{variation of double star $\mathcal{S}_{n}^2$} obtained by adding m (
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On the strength and independence number of powers of paths and cycles
(Azarbaijan Shahid Madani University, 2025-12-01)A numbering $f$ of a graph $G$ of order $n$ is a labeling that assigns distinct elements of the set $\left\{1,2, \ldots, n \right\}$ to the vertices of $G$. The strength $\mathrm{str}\left(G\right) $ of $G$ is defined by ...
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On co-maximal subgroup graph of $D_n$
(Azarbaijan Shahid Madani University, 2025-09-01)Let $G$ be a group and $S$ be the collection of all non-trivial proper subgroups of $G$. The co-maximal subgroup graph $\Gamma(G)$ of a group $G$ is defined to be a graph with $S$ as the set of vertices and two distinct ...
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Strong $k$-transitive oriented graphs with large minimum degree
(Azarbaijan Shahid Madani University, 2025-09-01)A digraph $D=(V,E)$ is $k$-transitive if for any directed $uv$-path of length $k$, we have $(u,v) \in E$. In this paper, we study the structure of strong $k$-transitive oriented graphs having large minimum in- or out-degree. ...
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Erratum to the paper ``A study on graph topology'' (Published in Commun. Comb. Optim. 8 (2023), no. 2, 397-409.)
(Azarbaijan Shahid Madani University, 2025-09-01)In this paper, we will point out errors in Theorem 2, Theorem 4, Theorem 5, Proposition 2, Proposition 3, Theorem 8, and Theorem 9 by giving suitable counterexamples. The statements of Theorem 2, Theorem 5, Proposition 2 ...
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A modified public key cryptography based on generalized Lucas matrices
(Azarbaijan Shahid Madani University, 2025-09-01)In this paper, we propose a generalized Lucas matrix (a recursive matrix of higher order) obtained from the generalized Fibonacci sequences. We obtain their algebraic properties such as direct inverse calculation, recursive ...
