We compute the Betti numbers of the edge rings of multi-path graphs using the induced-subgraph method introduced in [19]. Here, a multi-path graph refers to a simple graph consisting of two vertices and multiple paths...
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Degree Based Logical Adjacency Checking (DBLAC). An efficient coloring of graphs with unique logical AND operations. The logical AND operation shows More effective color assignment and fewer number of induced in the c...
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This paper presents a novel multicriteria shortest path search algorithm called Hierarchical MLS. The distinguishing feature of the algorithm is the multilayered structure of compressed k-Path-Cover graphs it operates...
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A mixed regular graph is a graph where every vertex has z incoming arcs, z outgoing arcs, and r edges;furthermore, if it has girth g, we say that the graph is a [z, r;g]-mixed graph. A [z, r;g]-mixed cage is a [z, r;g...
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We investigate the structure of graphs of twin-width at most 1, and obtain the following results: graphs of twin-width at most 1 are permutation graphs. In particular they have an intersection model and a linear struc...
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We investigate the chromatic number problem, a classic NP-complete problem identified by Karp among his 21 seminal problems. The chromatic number of a graph G is the smallest integer k such that each vertex of G can b...
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The famous Conway–Gordon–Sachs theorem for the complete graph on six vertices was extended to the general complete graph on n vertices by Kazakov–Korablev as a congruence modulo 2, and its integral lift was given b...
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Vulnerability measures and topological indices are crucial in solving various problems such as the stability of the communication networks and development of mathematical models for chemical compounds. In 1947, Harry ...
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A graph G is k-vertex-critical if χ(G) = k but χ(G − v) 1, H2)-free if it contains no induced subgraph isomorphic to H1 nor H2. A W4 is the graph consisting of a C4 plus an additional vertex adjacent to all the vert...
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Looped Transformers have shown exceptional neural algorithmic reasoning capability in simulating traditional graph algorithms, but their application to more complex structures like hypergraphs remains underexplored. H...
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