Clear, lively style covers all basics of theory and application, including mathematical models, elementary concepts of graph theory, transportation problems, connection problems, party problems, diagraphs and mathematical models, games and puzzles, graphs and social psychology, planar graphs and coloring problems, and graphs and other mathematics.
Here's a sample of other books in this Dover category
Introduction to Graph Theory by Richard J. Trudeau Aimed at "the mathematically traumatized," this text offers nontechnical coverage of graph theory, with exercises. Discusses planar graphs, Euler's formula, Platonic graphs, coloring, the genus of a graph, Euler walks, Hamilton walks, more. 1976 edition.
Planar Graphs: Theory and Algorithms by T. Nishizeki, N. Chiba This text features most of the important theorems and algorithms for planar graphs. Suitable as a textbook, it is also useful for researchers and includes an extensive reference section. 1988 edition.
Extremal Graph Theory by Bela Bollobas Concise yet comprehensive, this treatment of extremal graph theory is appropriate for undergraduate and graduate students and features numerous exercises and complete proofs. 1978 edition.
Pearls in Graph Theory: A Comprehensive Introduction by Nora Hartsfield, Gerhard Ringel Stimulating and accessible, this undergraduate-level text covers basic graph theory, colorings of graphs, circuits and cycles, labeling graphs, drawings of graphs, measurements of closeness to planarity, graphs on surfaces, and applications and algorithms. 1994 edition.