## Applications of graph theory to group structure |

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algorithm analysis articulation point balanced graph balancing process base with axis belong Cartesian product cells channels Chap clique commutative law complete algebraic graph consider constitute corresponding cost cycles defined definition degree of unbalance denoted e(xy e(xz elements equal equivalence class equivalence relation example exists Figure Flament function graph G graph of Fig Graph Theory Hamiltonian paths Harary hence homogeneous model information ah lattice Luce marked mathematical minimum balancing sets multi-graph negative edges negative triangles notion number of arcs obtained optimal organization order relation pair partial graph path y(xy positive possible problem Proof properties Psychol represented secondary information Shaw sociogram stochastic matrix strongly connected component strongly connected graph subgraph subset symmetric difference symmetric graph Table task task model Theorem theory of graphs tion track Q(xy type of connectivity unique valuation valued graph x-equivalent