000			02485nam a2200277 i 4500
003			CSPC
005			20260804152034.0
008			260804s2026 ph a b 000 0 eng d
040			_aCSPC _beng _cCSPC _erda
090			_aUTH BSAM R935s 2026
100	1		_aRull, Rodly Angelo S., _eauthor.
245	1	0	_aSome generator subgraphs of square tilings / _cRodly Angelo S. Rull.
300			_a113 leaves.
336			_2rdacontent _atext
337			_2rdamedia _aunmediated
338			_2rdacarrier _avolume
502			_aUndergraduate Thesis (BSAM)- Applied Mathematics. _cCamarines Sur Polytechnic Colleges, 2026.
504			_aIncludes bibliographical references.
520	3		_aAnalyzing the structure of graphs sometimes involves identifying specific sub- graphs that disclose important properties of the graph. One such concept is gen- erator subgraphs, which examine how certain subgraphs are capable of generat- ing the edges on a given graph. Necessary conditions are established for these square tilings to serve as generator subgraphs. All graphs considered in this pa- per are finite simple undirected graphs. Let H be a subgraph of G. Then the set EH(G) = {A ∈ E (G)|G[A] H} denotes the uniform set of H with respect to G while E (G) denotes the subspace of the edge space E (G) generated by EH(G), we adopt the symbol EH(G). The subgraph H of G is a generator subgraph if and only if, EH(G)is a generating set, that is EH(G) = E (G), then H is called a generator subgraph of G. The researcher established that the dimension of edge space of a square tiling is dim(E (□n×m)) = 2nm +n+ m, the cardinality of the uniform set of P4 with respect to □n×m is |EP4 (□n×m)| = 16nm − 6n − 6m. Moreover, this paper provides necessary and sufficient conditions for paths and disjoint union of paths to be generator subgraphs of square tilings. Specifically, this paper provides characterization for star, tadpole graph and hairy cycle, so that these classes of graphs are generator subgraphs of square tilings. The findings of this study contribute to a deeper understanding of a graph structure and its potential applications in various fields of graph theory.
720			_aMagtibay, Francis Gerard C., _eadviser.
720			_aNieva, Alex Ralph B., _echair, panelist.
720			_aJagmis, Jiel Mark D., _epanelist.
720			_aTorino, Jovanie G., _eexternal panelist.
942			_2ddc _n0 _cUM _hR935s _iBSAM _kUTH _m2026
999			_c32856 _d32856