Journal of Combinatorial Mathematics and Combinatorial Computing
ISSN: 0835-3026 (print) 2817-576X (online)
The Journal of Combinatorial Mathematics and Combinatorial Computing (JCMCC) embarked on its publishing journey in April 1987. From 2024 onward, it publishes four volumes per year in March, June, September and December. JCMCC has gained recognition and visibility in the academic community and is indexed in renowned databases such as MathSciNet, Zentralblatt, Engineering Village and Scopus. The scope of the journal includes; Combinatorial Mathematics, Combinatorial Computing, Artificial Intelligence and applications of Artificial Intelligence in various files.
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- Research article
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 009
- Pages: 161-166
- Published: 30/04/1991
- Research article
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 009
- Pages: 155-159
- Published: 30/04/1991
An \(h\)-cluster in a graph is a set of \(h\) vertices which maximizes the number of edges in the graph induced by these vertices. We show that the connected \(h\)-cluster problem is NP-complete on planar graphs.
- Research article
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 009
- Pages: 149-153
- Published: 30/04/1991
- Research article
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- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 009
- Pages: 141-147
- Published: 30/04/1991
Lee conjectures that for any \(k > 1\), a \((n,nk)\)-multigraph decomposable into \(k\) Hamiltonian cycles is edge-graceful if \(n\) is odd. We investigate the edge-gracefulness of a special class of regular multigraphs and show that the conjecture is true for this class of multigraphs.
- Research article
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 009
- Pages: 129-140
- Published: 30/04/1991
A balanced incomplete block design \(B[k, \alpha; v]\) is said to be a nested design if one can add a point to each block in the design and so obtain a block design \(B[k + 1, \beta; v]\). Stinson (1985) and Colbourn and Colbourn (1983) proved that the necessary condition for the existence of a nested \(B[3, \alpha; v]\) is also sufficient. In this paper, we investigate the case \(k = 4\) and show that the necessary condition for the existence of a nested \(B[4, \alpha; v]\), namely \(\alpha = 3\lambda\), \(\lambda(v – 1) \equiv 0 \pmod{4}\) and \(v \geq 5\), is also sufficient. To do this, we need the concept of a doubly nested design. A \(B[k, \alpha; v]\) is said to be doubly nested if the above \(B[k + 1, \beta; v]\) is also a nested design. When \(k = 3\), such a design is called a doubly nested triple system. We prove that the necessary condition for the existence of a doubly nested triple system \(B[3, \alpha; v]\), namely \(\alpha = 3\lambda\), \(\lambda(v – 1) \equiv 0 \pmod{2}\) and \(v \geq 5\), is also sufficient with the four possible exceptions \(v = 39\) and \(\alpha = 3, 9, 15, 21\).
- Research article
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 009
- Pages: 119-127
- Published: 30/04/1991
We exhibit here an infinite family of planar bipartite graphs which admit a \(k\)-graceful labeling for all \(k \geq 1\).
- Research article
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- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 009
- Pages: 107-118
- Published: 30/04/1991
It is shown that under certain conditions, the embeddings of chessboards in square boards, yield non-isomorphic associated graphs which have the same chro- matic polynomials. In some cases, sets of non-isomorphic graphs with this property are formed.
- Research article
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- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 009
- Pages: 97-106
- Published: 30/04/1991
A diagonal Latin square is a Latin square whose main diagonal and back diagonal are both transversals. In this paper we give some constructions of pairwise orthogonal diagonal Latin squares (PODLS). As an application of such constructions we improve the known result about three PODLS and show that there exist three PODLS of order \(n\) whenever \(n > 46\); orders \(2 \leq n \leq 6\) are impossible, the only orders for which the existence is undecided are: \(10, 14, 15, 18, 21, 22, 26, 30, 33, 34\) and \(46\).
- Research article
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 009
- Pages: 91-96
- Published: 30/04/1991
Finding the probability that there is an operational path between two designated vertices in a probabilistic computer network is known to be NP-hard. Edge-packing is an efficient strategy to compute a lower bound on the probability. We prove that finding the set of paths that produces the best edge-packing lower bound is NP-hard.
- Research article
- Full Text
- Journal of Combinatorial Mathematics and Combinatorial Computing
- Volume 009
- Pages: 79-89
- Published: 30/04/1991
Using a contraction method, we find some best-possible sufficient conditions for \(3\)-edge-comected simple graphs such that either the graphs have spanning eulerian subgraphs or the graphs are contractible to the Petersen graph.